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Meter Bridge Notes

Meter Bridge: A meter bridge, also known as a slide wire bridge, is a device that works on the Wheatstone bridge idea. A metre bridge is used to find the unknown resistance of a conductor. In Physics, while theory forms the basis of our knowledge, practicals form our understanding. What is this device? This is a   meter bridge! It consists of a wire of one meter, which is why it is called a ‘meter bridge’. It is used to measure the resistance of wires, coils or any other material. Please read on to learn about the meter bridge formula, meter bridge diagram, and more.

In this article, we will provide you with all information about the meter Bridge, the principle of the meter bridge, meter bridge experiment class 12 etc, continue to learn the concept thoroughly and make no mistakes while answering questions on the meter bridge.

What is Meter Bridge?

A meter bridge is an electrical apparatus using which we can measure the value of unknown resistance. It is made using a metre long wire of uniform cross-section. This wire is either nichrome or manganin or constantan because they offer high resistance and low-temperature coefficient of resistance.

A meter bridge or Slide wire bridge is designed from a Wheatstone bridge. It is the most basic and functional application of a Wheatstone bridge.

The Principle of Meter Bridge

A meter bridge works on the principle of a Wheatstone bridge. A Wheatstone bridge is based on the principle of null deflection, i.e. when the ratio of resistances in the two arms is equal, no current will flow through the middle arm of the circuit. Consider the diagram of the Wheatstone bridge as shown below. It consists of four resistances \(P,\,Q,\,R\) and \(S\) with a battery of EMF \(E\).

In the balanced condition, no current flows through the galvanometer, and terminals, \(B\) and \(D\) are at the same potential. This condition arises when, \(\frac{P}{Q} = \frac{R}{S}\)

Construction of a Meter Bridge

• A meter bridge has a \(1\,\rm{m}\) long wire of uniform cross-section area, which is stretched tight.
• Between two metal strips that are bent at right angles, this wire is then carefully clamped, as shown in the diagram below:
• Within the gap between the metal stripes, resistances are connected. In the first gap, \(R\), a resistance box, and in the second gap, a small resistor wire \(S\) is connected.
• The endpoints within which the wire is clamped are connected to a key through the cell.
• A galvanometer is connected to the metallic right in the middle of the two gaps.
• A jockey is connected at the other end of the galvanometer (Here, a jockey is a metal rod with a knife-like edge at one end that slides over the potentiometer wire to make an electrical connection). The jockey is slid over the meter bridge wire till the galvanometer shows zero deflection.

Meter Bridge Working

• To begin with, move the jockey to the endpoints of the wire, i.e., \(A\) and \(C\). The deflection of the galvanometer should be opposite on both ends.
• From side \(A\), start sliding the jockey slowly over the wire and carefully observe where the deflection of the galvanometer comes out to be zero.
• If such a point is not obtained, try varying the resistance across the bridge by changing the resistance on the variable resistance.
• Slide the jockey over the wire and carefully observe the point on the wire where the deflection of the galvanometer comes out to be zero. This is the null point as represented by the point ‘\(B\)’ in the diagram.
• Obtain the length of the null point using the meter scale attached along the wire. This is the ‘balancing length’ of the meter bridge.
• Let the distance between points \(A\) and \(B\) be ‘\(l_1\)’.
• Let the distance between points \(B\) and \(C\) be ‘\(l_2\)’, where \(l_2 = 100 – l_1.\)

When the galvanometer shows null deflection, the meter bridge behaves like a Wheatstone bridge and can be represented as:

Find the Resistance of the Given Wire by Metre Bridge

If \(S\) is the unknown resistance in the above circuit, we can calculate its value using the meter bridge. In the balanced condition, \(\frac{R}{{\text{Resistance}}\;{\text{across}}\;{\text{length}}\;AB} = \frac{S}{{\text{Resistance}}\;{\text{across}}\;{\text{length}}\;BC}\) We know that the resistance \(r\) of a wire of length \(l\), area of cross-section \(A\) and resistivity \(ρ\) is given as, \(r = \frac{{\rho l}}{A}.\) Using this relation, if \(ρ\) be the resistivity and \(A\) be the area of cross-section of the given meter bridge wire, then the resistance across length \(AB = \frac{{\rho l_1}}{A}.\) The resistance across length \(BC = \frac{{\rho l_2}}{A}.\) Substituting these values in the above relation, we get: \(\frac{R}{{\frac{{\rho {l_1}}}{A}}} = \frac{S}{{\frac{{\rho {l_2}}}{A}}}\) or, \(\frac{R}{{{l_1}}} = \frac{S}{{{l_2}}}\) \(\frac{R}{{{l_1}}} = \frac{S}{{100 – {l_1}}}\) Thus, the unknown resistance, \(S = \left( {100 – {l_1}} \right)\frac{R}{{{l_1}}}\) We can calculate the specific resistivity of the unknown resistance by using the formula, \(\rho = \frac{{\pi {d^2}S}}{{4L}}\) Where \(d\) is the diameter of the wire, \(S\) is the unknown resistance (of the wire), and \(L\) is the length of the wire.

Meter Bridge Experiment Class 12

Equipment Required

1. Meter Bridge 2. Galvanometer 3. Connecting wires 4. Unknown resistance 5. Resistance Box 6. Jockey 7. One-way key 8. Screw Gauge 9. Lechlanche cell

1. Collect all the required instruments and make all the necessary connections, as demonstrated in the above figure. 2. Take some appropriate kind of resistance out from the resistance box ‘\(R\)’. 3. Now, place the jockey at point \(A\); look that there is a deflection within the galvanometer. When the jockey is moved from point \(A\) to Point \(C\), the deflection of the galvanometer must go from one side to the other side. If it is not observed, adjust the known resistance value. 4. Start sliding the jockey from \(A\) towards \(C\) and obtain the point where the deflection of the galvanometer is zero. 5. Proceed with the above strategy for various values of the ‘\(R\)’. Note probably around \(5 -10\) readings. 6. The point where the galvanometer gives null deflection is the balance point of the meter bridge for the given unknown resistance. 7. Measure the distance between point \(A\) and the balance point of a given wire using an ordinary meter scale and the radius of the wire using a screw gauge (Take at least five readings for both the quantities). 8. Compute the mean value of the unknown resistances obtained above. It will be equal to the sum of all the values of resistance divided by the total number of readings taken.

Errors in the Meter Bridge

The most common error that can affect the measurement accuracy of a meter bridge is the end error . The end error can come up due to the following reasons:

1. We know that along the length of the bridge wire, a scale is provided. If the zero of the scale does not coincide with the starting point of the bridge wire, the \(100\,\rm{cm}\) mark on the scale will not coincide with the endpoint of the wire. This will lead to incorrect measurements of the balancing length. 2. The non-uniformity of the metal wire might lead to the generation of stray resistance, and it will create an end error.

We can minimize end error by taking multiple readings of the experiment by interchanging the unknown and known resistance in the circuit and by calculating the final value of resistance by taking the mean of all the observations.

Solved Examples of Meter Bridge

Q.1. In a meter bridge, there are two unknown resistance \(R\) and \(S\). Find the ratio of \(R\) and \(S\) if the galvanometer shows a null deflection at \(20\,\rm{cm}\) from one end? Ans: The null deflection in the galvanometer is obtained at \(20\,\rm{cm}\) from one end. Let, \(L_1 = 20\,\rm{cm}\) So, \(L_2 = 100 – 20 = 80\,\rm{cm}\) Thus, the ratio of unknown resistance will be: \(\frac{R}{{{L_1}}} = \frac{S}{{{L_2}}}\) Thus, \(\frac{R}{{{S}}} = \frac{1}{{{4}}}\)

Q.2. A \(20\,\rm{Ω}\) resistor is connected in the left gap, and an unknown resistance is joined in the right gap of the meter bridge. Also, the null deflection point is shifted by \(40\,\rm{cm}\) when the resistors are interchanged. Find the value of unknown resistance? Ans: In the first case, let the deflection point is taken as \(L\). Let the balance point gets shifted to \(l\) by \(40\,\rm{cm}\) when the resistors are interchanged. Thus, \(L – l = 40\,\rm{cm}\) Also, \(L + l = 100\,\rm{cm}\) Solving the above equations, we get: \(l = 30\,\rm{cm}\) \(L = 70\,\rm{cm}\) Let \(R = 20\,\rm{Ω}\) And unknown resistance be \(S\), thus, \(\frac{R}{S} = \frac{L}{l}\) \(\frac{R}{S} = \frac{70}{30}\) \(\frac{20}{S} = \frac{7}{3}\) \(∴ S = 8.57\,\rm{Ω}\)

A meter bridge is an electrical apparatus using which we can measure the value of unknown resistance. It is made using a metre long wire of uniform cross-section. This wire is either nichrome or manganin or constantan. The principle of working of a meter bridge is the same as the principle of a Wheatstone bridge. A Wheatstone bridge is based on the principle of null deflection. Thus, the unknown resistance, \(S = \left( {100 – {l_1}} \right)\frac{R}{{{l_1}}}.\)

FAQs on Meter Bridge

Q.1: What is the principle of meter bridge? Ans: Meter bridge is based on the principle of the Wheatstone bridge.

Q.2: Why do we use constantan or manganin wire in a meter bridge? Ans: Constantan, manganin, or nichrome wires provide a low-temperature coefficient of resistance, so they are used in a meter bridge.

Q.3: What is a meter bridge, and what is it used for? Ans: A meter bridge is an electrical apparatus that is used to measure the unknown resistance of a conductor. It consists of a wire of length of one meter. Hence it is called a meter bridge.

Q.4: What is the end error in a meter bridge? Ans: End error occurs when the zero scales of the meter scale do not coincide with the starting of the wire. It is caused due to the shifting of zero scale or the stray resistance in the wire.

Q.5: Give the formula to measure the unknown resistance for a meter bridge. Ans: The unknown resistance, \(S = \left( {100 – {l_1}} \right)\frac{R}{{{l_1}}}\), where \(R\) is known resistance and \(l_1\) is the balancing length of the wire.

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Chapter 1: Electric Charges and Fields

• Unit of Electric Charge
• Conductors and Insulators
• Charging by Induction
• Basic Properties of Electric Charge
• Coulomb's Law
• Electric Charge and Electric Field
• Electric Field Lines
• Electric Dipole
• Continuous Charge Distribution
• Gauss's Law
• Applications of Gauss's Law

Chapter 2: Electrostatic Potential and Capacitance

• Electric Potential Energy
• Electric Potential Due to a Point Charge
• Electric Potential Of A Dipole and System Of Charges
• Equipotential Surfaces
• Potential Energy of a System of Charges
• Potential Energy in an External Field
• Electrostatics of Conductors
• Dielectrics and Polarisation
• Capacitance
• What is a Parallel Plate Capacitor?
• Capacitors in Series and Parallel
• Energy stored in a Capacitor

Chapter 3: Current Electricity

• Electric Current in Conductors
• Drift Velocity
• Ohm's Law - Definition, Formula, Applications, Limitations
• Temperature Dependence of Resistance
• Electrical Energy and Power
• Resistors in Series and Parallel Combinations
• Electromotive Force
• Combination of Cells in Series and Parallel
• Meter Bridge - Explanation, Construction, Working, Sample Problems
• Potentiometer - Definition, Working Principle, Types

Chapter 4: Moving Charges and Magnetism

• Motion of a Charged Particle in a Magnetic Field
• Biot-Savart Law
• Ampere's Circuital Law and Problems on It
• Magnetic Field Due to Solenoid and Toroid
• Force between Two Parallel Current Carrying Conductors
• Current Loop as a Magnetic Dipole
• Moving Coil Galvanometer

Chapter 5: Magnetism and Matter

• Earth's Magnetic Field - Definition, Causes, Components
• Magnetization and Magnetic Intensity
• Diamagnetic Materials - Definition, Properties, Applications
• Permanent Magnets and Electromagnets

Chapter 6: Electromagnetic Induction

• Experiments of Faraday and Henry
• Faraday’s Laws of Electromagnetic Induction
• Motional Electromotive Force
• Energy Consideration
• What are Eddy Currents?
• Inductance - Definition, Derivation, Types, Examples
• AC Generator - Principle, Construction, Working, Applications

Chapter 7: Alternating Current

• AC Voltage Applied to a Resistor
• Phasors | Definition, Examples & Diagram
• AC Voltage Applied to an Inductor
• AC Voltage Applied to a Capacitor
• Series LCR Circuits
• Power in AC Circuit
• LC Oscillations
• Transformer

Chapter 8: Electromagnetic Waves

• Displacement Current
• Electromagnetic Waves
• Electromagnetic Spectrum

Chapter 9: Ray Optics and Optical Instruments

• Spherical Mirrors
• Refraction of Light
• Total Internal Reflection
• Image formation by Spherical Lenses

Chapter 10: Wave Optics

• Huygen's Wave Theory
• Superposition and Interference
• Young's Double Slit Experiment
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• Polarization of Light

Chapter 11: Dual Nature of Radiation and Matter

• Photoelectric Effect
• Experimental Study of Photoelectric Effect
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Chapter 12: Atoms

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Chapter 13: Nuclei

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Meter Bridge – Explanation, Construction, Working, Sample Problems

An electric flow is a flood of charged particles, like electrons or particles, traveling through an electrical conveyor or space. It is estimated as the net pace of stream of electric charge through a surface or into a control volume. The moving particles are called charge transporters, which might be one of a few sorts of particles, contingent upon the conductor. In electric circuits, the charge transporters are regularly electrons traveling through a wire. 

In semiconductors, they can be electrons or openings. In an electrolyte, the charge transporters are particles, while in plasma, an ionized gas, they are particles and electrons. The SI unit of electric flow is the ampere, or amp, which is the progression of electric charge across a surface at the pace of one coulomb each second. The ampere is a SI base unit Electric flow is estimated utilizing a gadget called an ammeter.  

Electric flows make attractive fields, which are utilized in engines, generators, inductors, and transformers. In normal conductors, they cause Joule warming, which makes light in radiant lights. Time-shifting flows emanate electromagnetic waves, which are utilized in media communications to communicate data.

Meter Bridge

A meter connect is an electrical contraption utilizing which we can quantify the worth of obscure obstruction. It is made utilizing a meter long wire of uniform cross-area. This wire is either nichrome or manganin or constantan since they offer high opposition and low-temperature coefficient of obstruction. A meter scaffold or Slide wire connect is planned from a Wheatstone connect. It is the most fundamental and useful utilization of a Wheatstone connect.

Principle of a Meter Bridge:

The rule of working of a meter connect is equivalent to the rule of a Wheatstone connect. A Wheatstone connect depends on the rule of invalid avoidance, for example at the point when the proportion of protections in the two arms is equivalent, no current will move through the centre arm of the circuit. 

Think about the outline of the Wheatstone connect as displayed underneath. It comprises four obstructions P, Q, R and S with a battery of emf E.

In the reasonable condition, no current moves through the galvanometer and terminals, B and D are at a similar potential. 

This condition emerges when, 

Construction of a Meter Bridge:

• A meter connect has a 1m long wire of uniform cross-segment region, which is extended tight.  
• Between two metal strips which are twisted at right points, this wire is then painstakingly clasped,  
• Inside the hole between the metal stripes, protections are associated. In the principal hole, R, an obstruction confine and the subsequent hole, little resistor wire S is associated.  
• The endpoints inside which the wire is clipped are associated with a key through the cell.  
• A galvanometer is associated with the metallic directly in the centre of the two holes.  
• A rider is associated at the opposite finish of the galvanometer (Here, a rider is a metal bar with a blade-like edge toward one side, slides over the potentiometer wire to make an electrical association). The rider is slid over the meter connect wire till the galvanometer shows zero diversion.

Construction of Meter Bridge

Working of a Meter Bridge:

• In any case, move the rider to the endpoints of the wire, i.e. A and C. The diversion of the galvanometer ought to be inverse on the two finishes.
• From side A, begin sliding the rider gradually over the wire and cautiously see where the redirection of the galvanometer comes out to be zero.  
• In the event that such a point isn’t acquired, take a stab at different obstructions across the extension by changing the opposition on the variable opposition.  
• Slide the rider over the wire and cautiously notice the point on the wire where the redirection of the galvanometer comes out to be zero. This is the invalid point as addressed by point ‘B’ in the graph.  
• Get the length of the invalid point utilizing the meter scale appended along the wire. This is the ‘adjusting length’ of the meter connected.  
• Leave the distance between focuses A n and B alone ‘l 1 ‘.  
• Leave the distance between focuses B and C alone ‘l 2 ‘, where l 2 =100–l 1 .  
• At the point when the galvanometer shows invalid diversion, the meter connects acts like a Wheatstone connects and can be addressed as:

Calculation of an Unknown Resistance Using Meter Bridge: In case S is the obscure opposition in the above circuit, we can ascertain it’s worth utilizing the meter connect. In reasonable condition, R / Resistance across length AB = S / Resistance across length BC We realize that the obstruction r of a wire of length l, space of cross-area An and resistivity ρ is given as,   r= ρ l / A Utilizing this connection, in case of ρ be the resistivity and A be the space of cross-part of the given meter connect wire, then, at that point the obstruction across the length,  AB=ρ l 1 / A The resistance across the length,  BC=ρ l 2 / A Subbing these qualities in the above connection, we get:  R / ρ l 1 / A = S / ρ l 2 / A  or  R / l 1 = S / l 2   R / l 1 = S / 100-l 1 Thus, the unknown resistance,  S= (100–l 1 ) R / l 1   We can ascertain the particular resistivity of the obscure obstruction by utilizing the equation,  ρ = πd 2 S / 4L  where d is the width of the wire, S is the obscure opposition (of the wire), and L is the length of the wire.

Sample Questions

Question 1: What is the end blunder in a meter connect?

End mistake happens when the no sizes of the meter scale don’t agree with the beginning of the wire. It is caused because of the moving of zero scale or the wanderer obstruction in the wire.

Question 2: What is a meter bridge, and what is it utilized for?

A meter bridge is an electrical apparatus that is used to measuring the unknown resistance of a conductor. It consists of a wire of length one meter. Hence it is called a meter bridge.

Question 3: In a meter bridge, there are two unknown resistance R and S. Find the ratio of R and S if the galvanometer shows a null deflection at 20cm from one end?

Answer: 

The null deflection in the galvanometer is obtained at 20cm from one end. Let, L1=20cm So, L2=100–20=80cm Thus, the ratio of unknown resistance will be: R / L1=S / L2 Thus, R / S=1 / 4

Question 4:  A 20Ω resistor is connected in the left gap, and an unknown resistance is joined in the right gap of the meter bridge. Also, the null deflection point is shifted by 40cm when the resistors are interchanged. Find the value of unknown resistance?

 In the first case, let the deflection point is taken as L. Let the balance point gets shifted to l by 40cm when the resistors are interchanged. Thus, L– l=40cm Also, L+ l=100cm Solving the above equations, we get: l=30cm L=70cm Let R=20Ω And unknown resistance be S, thus, R / S=L / l R / S=70 / 30 20 / S=7 / 3 ∴S=8.57Ω

Question 5: For what reason do we utilize constantan or manganin wire in a meter connect?

Constantan, manganin or nichrome wires give a low-temperature coefficient of obstruction, so they are utilized in a meter bridge.

Question 6: Give the equation to gauge the obscure obstruction for a meter connect

The unknown resistance, S=(100–l1) R / l1, where R is known resistance and l1 is the balancing length of the wire.

Question 7: In a meter bridge with a standard resistance of 15 Ω in the right gap, the ratio of balancing length is 3:2. Find the value of the other resistance.

Q=15 Ω , l1:l2 = 3:2 l1/l2 = 3/2 P/Q = l1/l2 P = Q x l1/l2 P= 22.5 Ω

Question 8: In a meter bridge, the value of resistance in the resistance box is 10 Ω. The balancing length is l1 = 55 cm. Find the value of unknown resistance.

Q= 10 Ω P/Q =l1/100-l1 P=Q x l1/100-l1 P= 10×55/100-55 P=12.2 Ω

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• Wheatstone Bridge, Meter Bridge and Potentiometer

Every other day, science presents us with one or more ways to feel amazed. There are a host of experiments that show both how we can use things and make newer things out of them. Experiments related to Wheatstone Bridge and the potentiometer are among few such things in science that invoke a curious sense of amazement. Let us study more about the concept of Wheatstone bridge and meter bridge, along with potentiometer.

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The concept of wheatstone bridge.

Defined simply, a Wheatstone Bridge is an electric circuit that is used to measure the electrical resistance of a circuit. The circuit is set out by balancing two legs of a bridge circuit. Out of the two, one of the legs is an unknown component which was invented by Samuel Hunter Christie in the year 1833 and later, it improved and popularized by Sir Charles Wheatstone in the year 1843.

Nowadays, technological progress has allowed us to make various measurements through sophisticated tools and machines. However, even today, the wheat bridge remains an authentic way to measure electric resistance, down to the closest milliohms as well.

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The Principle behind the Wheatstone Bridge

The usual arrangement of the Wheat stone bridge circuit has four arms. The bridge circuit where the arms are situated consist of electrical resistance. Out of these resistances, P and Q are the fixed electrical resistances and these two arms are the ratio arms. Next, A Galvanometer connects between the terminals B and D through a switch K 2 . The source of voltage of this arrangement is connected to the terminals A and C through a switch, K 1 .

A variable resistor S is connected between point C and D. The potential at point D is altered by adjusting the value of a variable resistor. If a variation in the electrical resistance value of arm CD is brought, the value of current I2 will also vary as the voltage across both A and C is fixed.

If we continue to adjust the variable resistance, a situation may come when the voltage drops across the resistor S that is I2. Here, S becomes exactly equal to the voltage drop across resistor Q that is I1. Q. So, the potential at point B becomes equal to the potential at point D hence the potential difference between these two points is zero hence current through galvanometer is nil. The deflection in the galvanometer is nil when the switch K2 is closed.

Applying Kirchoff’Law, in this condition,

How is the meter bridge experiment carried out using the wheatstone principle.

The meter bridge experiment uses the wheat bridge experiment to demonstrate the resistance of an unknown conductor or to make a comparison between two unknown resistors. Through the above-stated equation, one can easily decipher the specific resistance of a given material

Conclusions of the wheat stone bridge principle are:

According to the Wheatstone-bridge principle, the resistance of length AB/resistance of length BC = R / X

Let l be the length of wire between A and B and then (100 – l) is the length of wire between B and C. Here, P = ρl / A. Since the wire has a uniform cross-section and ρ is constant. Its resistance is proportional to the length. That is P ∝ l, and Q ∝ (100–l). So,

L / (100–l) = R / X

This is how to draw the values of X for different values of R and the mean value gives the value of unknown resistance X.

The Concept of Potentiometer

A potentiometer is an electric device which is used to regulate EMF and internal resistance of a given cell . This helps in providing a variable resistance and therefore, a variable potential difference arising between two points in an electric circuit. It is basically a three-terminal resistor device with an adjustable arm that increases or reduces the resistance in the loop.

Potentiometer (Source: Wikipedia)

Solved Examples for You

Question: Describe how a potentiometer works in an arrangement.

Answer: A potentiometer consists of a uniform wire AB of manganin or constantan that has a length of usually 10 m. it is kept stretched between copper stripes that are fixed on a wooden board by the side of a metre scale. The wire is then divided into ten segments each of 1 m length.

These segments join in series through metal strips between points A and B. A steady current is maintained in the wire AB by a constant source of EMF Eo, called driver cell, that connects between A and B through a rheostat. A jockey slides over the potentiometer wire which makes contact with the wire and cell.

Potentiometer (Source: Wikimedia)

Thus we can say that the potential difference across any portion of the potential of the potentiometer wire is directly proportional to the length of that portion provided the current is uniform.

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How to Calculate Unknown Resistance Using Meter Bridge

Last Updated: May 26, 2016

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 10 people, some anonymous, worked to edit and improve it over time. This article has been viewed 167,075 times.

A meter bridge is an apparatus used to find the resistance of a coil; you will find it as part of the tools of a physics lab.

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Meter Bridge

Wheatstone Bridge

Meter Bridge is an instrument that is used to find the unknown resistance of a coil or any other material. This bridge works under the principle of Wheatstone bridge. We know that the Wheatstone Bridge is used to measure the unknown resistance connected in a circuit. It consists of four resistors of which two resistors are known Resistors , one variable resistor and one unknown resistor. It also consists of a galvanometer. The bridge has two series-parallel arrangements of resistors. The figure of Wheatstone bridge is shown below:

Wheatstone bridge

It consists of four arms AD, DC, CB and BA which has fixed and variable resistors. Resistors resists the flow of electric current. Its measure is called resistance. Here R 1 and R 3 are the fixed resistors and R 2 is the variable resistor and R x is the unknown resistor. The variable resistor is the resistor which restricts and also can control the flow of electric current. It can control the flow of current by either increasing or decreasing the value of resistance. Here AD and BA are the ratio arms. A galvanometer is connected between the terminals D and B. So they are called as the Galvanometer Arm . As the cell is connected between the terminals A and C, it is called battery arm.

Here by adjusting the value of the variable resistor R 2 we will make the deflection in galvanometer as zero. The bridge is said to be balanced when no current flows through the galvanometer. When there is no current flowing through the bridge the potential difference or voltage between the points D and B is zero. Here the current flowing through the fixed resistor R 1 and the variable resistor R 2 is the same and is considered as I 1.  The current flowing through the fixed resistor R 3 and the unknown resistor Rx will be the same and is I 2. When the potential at D and B is the same, the voltage drop from the point A to D is equal to the voltage drop at from point A to point B.

By applying Kirchhoff’s law we get I 1 R 1 - I 2 R 3 = 0. That is I 1 R 1 = I 2 R 3 . Kirchhoff’s voltage law states that the algebraic sum of all voltages within the loop will be equal to zero.

Now the voltage drop from point C to point D is equal to the voltage drop from point C to B. So I 1 R 2 - I 2 R X = 0. Thus I 1 R 2 = I 2 R X.

Now divide the equations

Thus Rx = R 2 R 3  / R 1. Finally the unknown resistance is determined in terms of other known Resistors of the Bridge .

The applications of the Wheatstone bridge include strain gauge, thermistor, potentiometer , light detector etc. Wheatstone bridge are also used in operational amplifier as it can measure and amplify the small changes that takes place in resistors.

Meter bridge is also known as the Slide Wire Bridge . It consists of a wire whose length is one meter and has uniform cross sectional area. Now the wire is stretched along a meter scale. The bridge has two metallic strips which is in reverted L shape on either side of the wire. These metallic strips act as holders for the wire. The wire is being clamped to the strips.These two metallic strips are made up of metals like copper. The bridge consists of another metallic strip which is placed between those two strips with a gap between them. So totally there are five leads on the bridge.

Meter bridge

A resistance box R and an unknown resistance S is connected across the two gaps of the metallic strips as shown in the figure. One end of the galvanometer is connected to the middle lead of the metallic strip which is placed between the L shaped strips. The other end of the galvanometer is connected to a jockey. The jockey is used to slide on the bridge wire. It is a metal rod with one end as knife edge.

Now adjust the value of resistance in the resistance box and slide the jockey along the wire. This process is to be done until the galvanometer shows a zero or null deflection. Consider at point B the galvanometer showed zero deflection. So now the jockey is connected to the point B on the wire. Thus the distance from the point A to B is taken as L 1 cm. Then the distance from point B to point C is L 2 cm that is 100 - L 1 cm. Now the meter bridge becomes similar to the Wheatstone bridge. The meter bridge now is drawn as Wheatstone bridge for more clearance.

Meter bridge to Wheatstone bridge

We know that R = ρ L /A, where R is the resistance, ρ is the resistivity, L is the length of the wire and A is the area of cross section of the wire. So the resistance across the portion AB of the wire is R w L 1 and that the resistance across the point BC is R w (100 - L 1 ). R w is the resistance of the whole wire. That is according to Wheatstone bridge we get

This is the equation

So to find the unknown resistance S we have S = R (100 - L 1 ) / L 1

Lab Experiment

If we are doing the meter bridge experiment in the lab, by adjusting the value of resistance box the galvanometer will show the null deflection. Then we will find the value of L 1 and L 2. After substituting these values in the equation we will find the unknown resistance. Now the process is being repeated for a number of values of resistance by adjusting the values resistance box. Then finally we will get the actual unknown resistance by calculating the mean of the unknown resistance. That is, total sum of unknown resistance / no of times the readings have been taken.

Also the specific resistivity of the material of the wire is ρ = π r 2 X/L, where r is the radius of the wire, X is the unknown resistance and L is the length of the wire.  

Problem Related with Meter Bridge

Q1.  In a meter bridge, there are two unknown resistance R 1 and R 2.   Find the ratio of R 1 and R 2 if the galvanometer shows a null deflection at 30 cm from one end?

The null deflection in the galvanometer is given as 30 cm from one end.

So consider L 1 = 30 cm

So L 2 = 100 – 30 = 70 cm

Thus the ratio of the unknown resistance can be found as

Thus R 1 : R 2 = 3: 7

Q2.  In the meter bridge, the null deflection is shown on the galvanometer which is at a distance of 30 cm from one point. When a known resistance of 10 Ω is connected in parallel with another unknown resistance S the null deflection shows at 50 cm from the same point. Find the unknown resistance of R and S.

In the first case L 1 = 30 cm

As the resistors are connected in parallel we know that the equivalent resistance is R 1 R 2 / R 1 + R 2

 = 10 * S / 10 + S

In the second case L 1 = 50 cm So L 2  = 100 – 50 = 50

So according to the formula

= R / (10 S / 10 + S) = 1

So R = 10 S / 10 + S

Substituting the value of R in equation 1we get

From equation 1 we get

Q3.  A 20 Ω resistor is connected in the left gap and an unknown resistance is connected in the right gap of the meter bridge. Also the null deflection point is shifted by 40 cm when the resistors are interchanged. Find the value of unknown resistance?

In the first case the deflection point is taken as L 1. Let the balance point gets shifted to L 2 by 40 cm when the resistors are interchanged.

So we get L 1 - L 2 = 40

Also we know L 1 + L 2 = 100

Solving these two equations we get L 2 = 30 cm and L 1 = 70 cm.

The meter bridge uses the same principle as the Wheatstone Bridge .

It is used to find the unknown Resistance of the Material .

The meter bridge consists of a wire of 100 cm, a scale, one unknown Resistor , one known Resistor or a Resistance Box , a Galvanometer and a jockey.

For finding the unknown Resistance, connect everything as required. Now until the galvanometer shows a zero or null deflection, adjust the value of resistance in the resistance box and slide the jockey through the wire. Measure the length of the wire L 1 at which the galvanometer showed null deflection. Calculate the length L 2.  Then by using the Wheatstone bridge principle we can find the unknown Resistance of the Meter Bridge . The Meter Bridge is also known as Slide Wire Bridge .

Watch this Video for more reference

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Determination of the specific resistance of a wire using a metre bridge

Introduction

Experimental Data

Reading of the balance point

Calculation

Percentage of error

• The wire used may not be uniform area of cross-section. So, it is essential to choose a suitable wire.
• Effect of end resistance due to copper strips, connecting screws, may affect the measurement. So, it is essential for taking proper measurement.
• All the connections and plugs must be tight.
• Jockey must be moved gently over the metre bridge wire.
• Null point may be far away from the middle.
• It is essential to take determine the diameter of the wire accurately.
• E.M.F of the cell must check before starting the experiment. The E.M.F of cell must be constant.
• The length measurements l and l΄ may have error if the metre bridge wire taut and along the scale in the metre bridge. So, it must be ensure to taut the metre bridge along the scale.
• The resistance of end pieces/metal strips may not be negligible. The error introduced by it can be reduced by interchanging the known and unknown resistance in gaps.[6]
• The percentage of error increases if the resistance box or other materials may not be clean. So, all the materials must be clean.
• The reading of screw gauge might be accurate.

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Experiment - to find resistivity of the material of a given wire using metre-bridge. - all with video answers.

Chapter Questions

Problem 2845

In meter bridge experiment, A thin uniform wire $\mathrm{AB}$ of length $1 \mathrm{~m}$ and unknown resistance $\mathrm{x}$ and a resistance of $12 \Omega$ are connected. In the above question, after appropriate conditions are made, it is found that no deflection takes places in the galvanometer when the sliding jockey touches the wire at a distance of $60 \mathrm{~cm}$ from $\mathrm{A}$. What is the value of the resistance $\mathrm{X}$ ? (A) $18 \Omega$ (B) $8 \Omega$ (C) $16 \Omega$ (D) $4 \Omega$

Problem 2846

A thin uniform wire $\mathrm{AB}$ of length $1 \mathrm{~m}$, an unknown resistance $\mathrm{X}$ and a resistance of $12 \Omega$ are connected by thick conducting strips as shown in figure. A battery and a galvanometer (with a sliding jockey connected to it) are also available. Connections are to measure the unknown resistance $\mathrm{X}$ using the principle of Wheatstone bridge. The appropriate connections are. (E Is the balance point for Wheatstone bridge) (A) battery across $E B$ and galvanometer across $B C$ (B) battery across $\mathrm{EC}$ and galvanometer across $\mathrm{BD}$ (C) battery across $\mathrm{BD}$ and galvanometer across $\mathrm{EC}$ (D) battery across $\mathrm{BC}$ and galvanometer across $\mathrm{CD}$

Problem 2847

A wire is in the form of a tetrahedron shown in figure. The resistance of each wire is $\mathrm{R}$. What is the resistance of the frame between the corners $\mathrm{A}$ and $\mathrm{B}$. (A) $(2 \mathrm{R} / 3)$ (B) $2 \mathrm{R}$ (C) $\mathrm{R}$ (D) $(\mathrm{R} / 2)$

Problem 2848

For the electrical circuit shown in the figure, the potential difference across the resistor of $400 \Omega$ as will be measured by the voltmeter $\mathrm{V}$ of resistance 400 is $\ldots \ldots \ldots$ (A) $(10 / 3) \mathrm{V}$ (B) $4 \mathrm{~V}$ (C) $(20 / 3) \mathrm{V}$ (D) $5 \mathrm{~V}$

Problem 2849

In a simple meter-bridge circuit, the both gaps are bridge by coils $\mathrm{P}$ and $\mathrm{Q}$ having the smaller resistance. A balance is obtained when the jockey key makes contact at a point of the bridge wire $40 \mathrm{~cm}$ from the $\mathrm{P}$ end. On shunting the coil $\mathrm{Q}$ with a resistance of $50 \Omega$ the balance point is moved through $10 \mathrm{~cm}$. What are the resistance of $\mathrm{P}$ and $\mathrm{Q}$ ? (A) $[(100) / 3] \Omega,[(100) / 2] \Omega$ respectively (B) $[(50) / 3] \Omega,[(50) / 2] \Omega$ respectively (C) $[(25) / 3] \Omega,[(25) / 2] \Omega$ respectively (D) $[(75) / 3] \Omega,[(75) / 2] \Omega$ respectively

Problem 2850

What is the resistance of an open key? (A) $\infty$ (B) Can't be determined (C) 0 (D) depends on the other resistance in the circuit

Problem 2851

What is the unit of temperature coefficient of resistance? (A) $\Omega^{-1}{ }^{\circ} \mathrm{C}$ (B) $\Omega^{1}{ }^{\circ} \mathrm{C}^{-1}$ (C) ${ }^{\circ} \mathrm{C}^{-1}$ (D) $\Omega^{0}{ }^{\circ} \mathrm{C}^{-1}$

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Meter Bridge Resistance of a Wire

Physics Practicals Class 12

Meter Bridge – Resistance of a Wire

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About Simulation

• In this simulation, you will correlate the principle of Wheatstone bridge with the meter bridge experiment for physics practical class 12.
• You will learn the theory behind Wheatstone’s meter bridge and examine the resistance of a wire.
• You will determine the resistivity (specific resistance) of a given material of the wire.
• All the experiment steps and procedures, such as connecting the wire, measuring the balancing lengths, observing the null deflection of the galvanometer, etc., are highly interactive and have been precisely recreated in a manner that is very similar to what you would do in a real lab.

• This interaction provides a very immersive virtual reality environment and gives you a real-lab-like experience while conducting or performing experiments.

Simulation Details

Description

The meter bridge, also known as the slide wire bridge consists of a 1-meter-long wire of uniform cross-sectional area, fixed on a wooden block. A scale is attached to the block. Two gaps are formed on it by using thick metal strips in order to make the Wheatstone bridge.

The meter bridge operates using the Wheatstone principle. Here, four resistors P, Q, R, and S are connected to form the network ABCD. Terminals A and C are connected to a battery, and the terminals B and D are connected to a galvanometer.

In the balancing condition, there is no deflection on the galvanometer. Then, $$\frac{P}{Q}=\frac{R}{S}$$

If a resistance wire of unknown resistance 𝑋 is introduced in the right gap of the meter bridge and the high resistance 𝑅 is introduced in the left gap of the meter bridge, then as the jockey slides over the bridge wire, it shows zero deflection at the balancing point (null point).

If the balancing length is 𝑙, then according to the Wheatstone principle, we have $$\frac{X}{R}=\frac{l}{100-l}$$

The unknown resistance is given by $$X=R \frac{l}{100-l}$$

The specific resistance of the wire can be calculated using the relation, $$\rho=\frac{\pi r^2 X}{L}$$

where, 𝐿 is the length of the wire and 𝑟 is its radius.

Requirements for this Science Experiment

⦁ Meter Bridge ⦁ Jockey ⦁ Resistance Box ⦁ Plug Key ⦁ Battery

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What is the use of the meter bridge experiment?

U se of meter bridge experiment: the meter bridge experiment is used to test resistance laws and figure out unknown resistances. explanation: meter bridge wire is made of alloy manganin, copper-nickel alloy (constantan), and nickel, chromium, and iron alloys (nichrome) because they are corrosion resistant. they have extremely cold temperatures. they have a high melting point of roughly 1400 degrees celsius. a meter bridge is an electrical device that is used to assess a conductor's resistance. it may also be used to determine the parallel and series equivalents of resistances..

In an experiment on meter bridge, if the balancing length AC is 'x'. what would be be its value, when the diameter on the meter bridge wire AB is made half ? Justify your answer.

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June 17, 2024

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Seawall baffles and AI help emerald shiners swim to Lake Erie

by Tom Dinki, University at Buffalo

University at Buffalo researchers are looking down at a 24-foot-long flume of shallow running water. Inside, about a dozen emerald shiner minnows are furiously attempting to swim against the current.

It's not going well for the shiners.

These tiny prey fish have sustained swim speeds of about 0.4 meters per second—with burst speeds up to double that—but the flume's current is running at about 0.4 meters per second, so, despite all their effort, the shiners swim to remain in place.

Yet some force starts to bring these disparate fish together. A group of two joins a group of eight, which then joins up with another group of four. Only once all 14 shiners are swimming together in tight formation do they finally begin to move upstream.

Video of this experiment will be fed into artificial intelligence tools that can track the movement of individual fish, as well as the velocity of the water.

This kind of data was the basis for the construction of an unconfined fishway along the seawall at Buffalo's Freedom Park, located near the Peace Bridge, in 2022. Ten steel, trapezoid-shaped baffles attached to the wall slow the Niagara River's velocity to allow emerald shiners to swim more easily upstream to Lake Erie, where they contribute to the health of the ecosystem including threatened birds and sport fish.

These results were described in a study published in Ecological Engineering .

Now, the U.S. Army Corps of Engineers is preparing to place baffles on the remaining 700 feet of seawall. The $5–10 million project is currently out for bid.

In addition to helping wild emerald shiners and the rest of the Niagara River ecosystem, UB researchers' ongoing experiments with the flume and AI can shed light on fundamental aspects of all fish behavior.

"We're trying to understand what determines a fish moving from Point A to Point B. Is it responding to the flow velocity or turbulence? Or is it responding to something else?" says one of the researchers, Sean Bennett, Ph.D., professor in the UB Department of Geography and associate dean in the UB College of Arts and Sciences.

"I'm convinced that the moment that two fish see each other in the flume, their behaviors change. Rightly or wrongly, I think all fish are responding to each other."

Collecting data for fishway construction

Emerald shiners, or Notropis atherinoides, are about finger length. They're commonly used as bait.

"Despite their size, they're crucial to sustaining other wildlife in the Niagara River and Great Lakes," Bennett says.

The engineered seawall at Freedom Park had previously been identified as a barrier to the shiners' migration to Lake Erie. The depth-averaged velocities adjacent to the seawall range from 0.8 to 1.2 meters per second, much faster than emerald shiners' sustained swim speeds.

The solution seemed to be an unconfined fishway along the wall with lower velocities, but how low? And would the shiners even use it?

Bennett and his team answered these questions via their recirculating flume. Constructed by Kevin Cullinan of the College of Arts and Sciences Instrument Machine Shop, the structure can mimic real aquatic environments and has been used to study everything from soil erosion to how marine mussels engineer riverbeds.

"It would be virtually impossible to do this research in the field. Emerald shiners are extremely fragile fish, so implanting any kind of tracking device is out of the question," says Bennett, who manages the flume. "In addition, we can ensure our results are precise and reproducible, and that's what the scientific community expects from experimental research."

Another advantage of the flume is that it allowed the researchers to use AI to analyze the position of the fish in relation to the baffles and the velocity of the water. Using video taken by a mounted camera above the flume, an object detection model correctly identified fish in the frame 94% of the time. The video was also used to decipher velocity by tracking the movement of particles in the water.

"From one video image, we can determine the location of the fish and the instantaneous flow field around that fish," says Adam Grodek, a Ph.D. student in the Department of Geography and member of the research team.

Following experiments, the model found evidence that the fish in the flume generally swam upstream and toward the baffles and chose to remain near the baffles.

Relying on that data, baffles were installed at Freedom Park, previously known as Broderick Park.

Results from researchers' study show the baffles reduced the nearshore flow velocities to about 0.4 to 0.6 meters per second, within the acceptable range of velocities for the shiners. Large number of shiners were observed swimming upstream along the seawall baffles, whereas shiners away from the wall were observed being overpowered by the current and carried downstream.

Exploring the fundamentals of fish behavior

Swimming together in a school can help fish reduce friction and more easily traverse rough waters. It's not unlike a group of birds or even fighter jets moving in a V formation to improve their aerodynamics.

But how do fish know to do this?

That's one of the fundamental questions Bennett's team is now using the flume and AI to help answer.

Bennett and Grodek are collaborating with Joseph Atkinson, Ph.D., professor in the Department of Civil, Structural and Environmental Engineering, School of Engineering and Applied Sciences. Other collaborators include the Army Corps of Engineers Buffalo District and SUNY Buffalo State University.

The team is currently training an object detection model to track fish even as they move in crisscrossing patterns. Once the data are collected, an agent-based model will be built to simulate this movement.

"It's similar to studying how people would leave a movie theater if someone yelled 'fire.' You can create rules of how agents interact with other agents as a way of navigating this spatial domain," Bennett said.

There's still much that scientists don't know about how fish coordinate their movements to maintain the shape of their school. Are they reacting to other fish's movements or are they simply following the path of lower turbulence?

"We don't yet know the magnitude to which groups of fish change their behavior," Bennett says. "We're really interested in how to separate an individual fish's behavior and its transition to group behavior."

Journal information: Ecological Engineering

Provided by University at Buffalo

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