observation in ohm's law experiment

Verification of Ohm’s Law experiment with data and graph

In the previous article, we discussed Ohm’s Law of current electricity. In this article, we’re going to perform an experiment for the verification of Ohm’s law. This practical verification of Ohm’s law is very important for the students of grades 10 and 12. This is a lab-based experiment to verify Ohm’s law or Ohm’s law practical.

Aim of the Experiment

Theory of the ohm’s law experiment.

From Ohm’s law , we know that the relation between electric current and potential difference is V = IR

or, \color{Blue}R=\frac{V}{I} ………….. (1)

or, resistivity, \color{Blue}\rho = \frac{RA}{L} ………. (2)

Where A is the cross-section area of the wire. A = πr 2 where r is the radius of the wire. L is the length of the wire.

Apparatus Used

The apparatus used for this experiment –

Circuit Diagram

Here, R is the resistance of the wire, A is the ammeter, V is the Voltmeter, Rh is the rheostat and K is the key. The arrow sign indicates the direction of the current flow in the circuit .

Formula used for the Ohm’s law lab experiment

\color{Blue}R = \frac{V}{I} ………….. (1) and \color{Blue}\rho = \frac{RA}{L} ………. (2)

Experimental data

The least count of Voltmeter = Smallest division of voltmeter = 0.05 Volt

We also need to plot I-V graph to confirm the experimental value of R.

Current versus Voltage graph (Ohm’s Law graph)

If we plot the Current as a function of voltage with the help of the above data then we will get a straight line passing through the origin.

Calculations

Calculation of resistance from the graph.

The inverse of the I-V graph gives the resistance of the wire. Now, from the graph, change in current, ∆I = AB = 0.5 amp corresponding change in voltage, ∆V = BC = 0.5 volt Thus, the Resistance from the graph, R = ∆V/∆I = 0.5/0.5 = 1.00 ohm

Calculation of resistivity of the wire

Length of the wire is, L = 50 cm = 0.5 m Radius of the wire. r = 0.25 mm = 0.25 × 10 -3 m So, the cross-section area of the wire, A = πr 2 = 3.14 × (0.25×10 -3 ) 2 = 0.196 × 10 -6 m 2 Thus from the equation-2 we get the resistivity of the material of the wire is, \rho = (1 × 0.196 ×10 -6 )/0.5 or, \rho = 0.392 × 10 -6 = 3.92 ×10 -7 ohm.m Thus the resistivity of the material of the wire is 3.92 ×10 -7 ohm.m

Final result

The resistance of the wire from the Current-Voltage graph is, R = 1.00 ohm The calculated value of the resistance of the wire is, R = 1.02 ohm. Resistivity of the material of the wire is 3.92 ×10 -7 ohm.m

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9.5: Ohm's Law

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Learning Objectives

By the end of this section, you will be able to:

• Describe Ohm’s law
• Recognize when Ohm’s law applies and when it does not

We have been discussing three electrical properties so far in this chapter: current, voltage, and resistance. It turns out that many materials exhibit a simple relationship among the values for these properties, known as Ohm’s law. Many other materials do not show this relationship, so despite being called Ohm’s law, it is not considered a law of nature, like Newton’s laws or the laws of thermodynamics. But it is very useful for calculations involving materials that do obey Ohm’s law.

Description of Ohm’s Law

The current that flows through most substances is directly proportional to the voltage V applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied :

\[I \propto V.\]

This important relationship is the basis for Ohm’s law . It can be viewed as a cause-and-effect relationship, with voltage the cause and current the effect. This is an empirical law, which is to say that it is an experimentally observed phenomenon, like friction. Such a linear relationship doesn’t always occur. Any material, component, or device that obeys Ohm’s law, where the current through the device is proportional to the voltage applied, is known as an ohmic material or ohmic component. Any material or component that does not obey Ohm’s law is known as a nonohmic material or nonohmic component.

Ohm’s Experiment

In a paper published in 1827, Georg Ohm described an experiment in which he measured voltage across and current through various simple electrical circuits containing various lengths of wire. A similar experiment is shown in Figure \(\PageIndex{1}\). This experiment is used to observe the current through a resistor that results from an applied voltage. In this simple circuit, a resistor is connected in series with a battery. The voltage is measured with a voltmeter, which must be placed across the resistor (in parallel with the resistor). The current is measured with an ammeter, which must be in line with the resistor (in series with the resistor).

In this updated version of Ohm’s original experiment, several measurements of the current were made for several different voltages. When the battery was hooked up as in Figure \(\PageIndex{1a}\), the current flowed in the clockwise direction and the readings of the voltmeter and ammeter were positive. Does the behavior of the current change if the current flowed in the opposite direction? To get the current to flow in the opposite direction, the leads of the battery can be switched. When the leads of the battery were switched, the readings of the voltmeter and ammeter readings were negative because the current flowed in the opposite direction, in this case, counterclockwise. Results of a similar experiment are shown in Figure \(\PageIndex{2}\).

In this experiment, the voltage applied across the resistor varies from −10.00 to +10.00 V, by increments of 1.00 V. The current through the resistor and the voltage across the resistor are measured. A plot is made of the voltage versus the current, and the result is approximately linear. The slope of the line is the resistance, or the voltage divided by the current. This result is known as Ohm’s law :

\[V = IR \label{Ohms}\]

where V is the voltage measured in volts across the object in question, I is the current measured through the object in amps, and R is the resistance in units of ohms. As stated previously, any device that shows a linear relationship between the voltage and the current is known as an ohmic device. A resistor is therefore an ohmic device.

Example \(\PageIndex{1}\): Measuring Resistance

A carbon resistor at room temperature \((20^oC)\) is attached to a 9.00-V battery and the current measured through the resistor is 3.00 mA. (a) What is the resistance of the resistor measured in ohms? (b) If the temperature of the resistor is increased to \(60^oC\) by heating the resistor, what is the current through the resistor?

(a) The resistance can be found using Ohm’s law. Ohm’s law states that \(V = IR\), so the resistance can be found using \(R = V/I\).

(b) First, the resistance is temperature dependent so the new resistance after the resistor has been heated can be found using \(R = R_0 (1 + \alpha \Delta T)\). The current can be found using Ohm’s law in the form \(I = V/R\).

• Using Ohm’s law and solving for the resistance yields the resistance at room temperature: \[R = \dfrac{V}{I} = \dfrac{9.00 \, V}{3.00 \times 10^{-3} A} = 3.00 \times 10^3 \, \Omega = 3.00 k\Omega\]
• The resistance at \(60^oC\) can be found using \(R = R_0 (1 + \alpha \Delta T)\) where the temperature coefficient for carbon is \(\alpha = -0.0005\). \[R = R_0 (1 + \alpha \Delta T) = 3.00 \times 10^3 (1 - 0.0005 (60^oC - 20^oC)) = 2.94 \, k\Omega.\] The current through the heated resistor is \[I = \dfrac{V}{R} = \dfrac{9.00 \, V}{2.94 \times 10^3 \, \Omega} = 3.06 \times 10^{-3} A = 3.06 \, mA.\]

Significance

A change in temperature of \(40^oC\) resulted in a 2.00% change in current. This may not seem like a very great change, but changing electrical characteristics can have a strong effect on the circuits. For this reason, many electronic appliances, such as computers, contain fans to remove the heat dissipated by components in the electric circuits.

Exercise \(\PageIndex{1}\)

The voltage supplied to your house varies as \(V(t) = V_{max} sin \, (2\pi \, ft)\). If a resistor is connected across this voltage, will Ohm’s law \(V = IR\) still be valid?

Yes, Ohm’s law is still valid. At every point in time the current is equal to \(I(t) = V(t) /R\), so the current is also a function of time, \(I(t) = \dfrac{V_{max}}{R} \, sin \, (2\pi \, ft)\).

Simulation: PhET

See how Ohm’s law (Equation \ref{Ohms}) relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm’s law. The sizes of the symbols in the equation change to match the circuit diagram.

Nonohmic devices do not exhibit a linear relationship between the voltage and the current. One such device is the semiconducting circuit element known as a diode . A diode is a circuit device that allows current flow in only one direction. A diagram of a simple circuit consisting of a battery, a diode, and a resistor is shown in Figure \(\PageIndex{3}\). Although we do not cover the theory of the diode in this section, the diode can be tested to see if it is an ohmic or a nonohmic device.

A plot of current versus voltage is shown in Figure \(\PageIndex{4}\). Note that the behavior of the diode is shown as current versus voltage, whereas the resistor operation was shown as voltage versus current. A diode consists of an anode and a cathode. When the anode is at a negative potential and the cathode is at a positive potential, as shown in part (a), the diode is said to have reverse bias. With reverse bias, the diode has an extremely large resistance and there is very little current flow—essentially zero current—through the diode and the resistor. As the voltage applied to the circuit increases, the current remains essentially zero, until the voltage reaches the breakdown voltage and the diode conducts current. When the battery and the potential across the diode are reversed, making the anode positive and the cathode negative, the diode conducts and current flows through the diode if the voltage is greater than 0.7 V. The resistance of the diode is close to zero. (This is the reason for the resistor in the circuit; if it were not there, the current would become very large.) You can see from the graph in Figure \(\PageIndex{4}\) that the voltage and the current do not have a linear relationship. Thus, the diode is an example of a nonohmic device.

Ohm’s law is commonly stated as \(V = IR\), but originally it was stated as a microscopic view, in terms of the current density, the conductivity, and the electrical field. This microscopic view suggests the proportionality \(V \propto I\) comes from the drift velocity of the free electrons in the metal that results from an applied electrical field. As stated earlier, the current density is proportional to the applied electrical field. The reformulation of Ohm’s law is credited to Gustav Kirchhoff, whose name we will see again in the next chapter.

9.4 Ohm's Law

Learning objectives.

By the end of this section, you will be able to:

• Describe Ohm’s law
• Recognize when Ohm’s law applies and when it does not

We have been discussing three electrical properties so far in this chapter: current, voltage, and resistance. It turns out that many materials exhibit a simple relationship among the values for these properties, known as Ohm’s law. Many other materials do not show this relationship, so despite being called Ohm’s law, it is not considered a law of nature, like Newton’s laws or the laws of thermodynamics. But it is very useful for calculations involving materials that do obey Ohm’s law.

Description of Ohm’s Law

The current that flows through most substances is directly proportional to the voltage V applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied :

This important relationship is the basis for Ohm’s law . It can be viewed as a cause-and-effect relationship, with voltage the cause and current the effect. This is an empirical law, which is to say that it is an experimentally observed phenomenon, like friction. Such a linear relationship doesn’t always occur. Any material, component, or device that obeys Ohm’s law, where the current through the device is proportional to the voltage applied, is known as an ohmic material or ohmic component. Any material or component that does not obey Ohm’s law is known as a nonohmic material or nonohmic component.

Ohm’s Experiment

In a paper published in 1827, Georg Ohm described an experiment in which he measured voltage across and current through various simple electrical circuits containing various lengths of wire. A similar experiment is shown in Figure 9.19 . This experiment is used to observe the current through a resistor that results from an applied voltage. In this simple circuit, a resistor is connected in series with a battery. The voltage is measured with a voltmeter, which must be placed across the resistor (in parallel with the resistor). The current is measured with an ammeter, which must be in line with the resistor (in series with the resistor).

In this updated version of Ohm’s original experiment, several measurements of the current were made for several different voltages. When the battery was hooked up as in Figure 9.19 (a), the current flowed in the clockwise direction and the readings of the voltmeter and ammeter were positive. Does the behavior of the current change if the current flowed in the opposite direction? To get the current to flow in the opposite direction, the leads of the battery can be switched. When the leads of the battery were switched, the readings of the voltmeter and ammeter readings were negative because the current flowed in the opposite direction, in this case, counterclockwise. Results of a similar experiment are shown in Figure 9.20 .

In this experiment, the voltage applied across the resistor varies from −10.00 to +10.00 V, by increments of 1.00 V. The current through the resistor and the voltage across the resistor are measured. A plot is made of the voltage versus the current, and the result is approximately linear. The slope of the line is the resistance, or the voltage divided by the current. This result is known as Ohm’s law :

where V is the voltage measured in volts across the object in question, I is the current measured through the object in amps, and R is the resistance in units of ohms. As stated previously, any device that shows a linear relationship between the voltage and the current is known as an ohmic device. A resistor is therefore an ohmic device.

Example 9.8

Measuring resistance.

(b) First, the resistance is temperature dependent so the new resistance after the resistor has been heated can be found using R = R 0 ( 1 + α Δ T ) R = R 0 ( 1 + α Δ T ) . The current can be found using Ohm’s law in the form I = V / R I = V / R .

• Using Ohm’s law and solving for the resistance yields the resistance at room temperature: R = V I = 9.00 V 3.00 × 10 −3 A = 3.00 × 10 3 Ω = 3.00 k Ω . R = V I = 9.00 V 3.00 × 10 −3 A = 3.00 × 10 3 Ω = 3.00 k Ω .
• The resistance at 60 ° C 60 ° C can be found using R = R 0 ( 1 + α Δ T ) R = R 0 ( 1 + α Δ T ) where the temperature coefficient for carbon is α = −0.0005 α = −0.0005 . R = R 0 ( 1 + α Δ T ) = 3.00 × 10 3 ( 1 − 0.0005 ( 60 ° C − 20 ° C ) ) = 2.94 k Ω R = R 0 ( 1 + α Δ T ) = 3.00 × 10 3 ( 1 − 0.0005 ( 60 ° C − 20 ° C ) ) = 2.94 k Ω . The current through the heated resistor is I = V R = 9.00 V 2.94 × 10 3 Ω = 3.06 × 10 −3 A = 3.06 mA . I = V R = 9.00 V 2.94 × 10 3 Ω = 3.06 × 10 −3 A = 3.06 mA .

Significance

Check your understanding 9.8.

The voltage supplied to your house varies as V ( t ) = V max sin ( 2 π f t ) V ( t ) = V max sin ( 2 π f t ) . If a resistor is connected across this voltage, will Ohm’s law V = I R V = I R still be valid?

Interactive

See how the equation form of Ohm’s law relates to a simple circuit by engaging the simulation below. Adjust the voltage and resistance, and see the current change according to Ohm’s law. The sizes of the symbols in the equation change to match the circuit diagram.

Nonohmic devices do not exhibit a linear relationship between the voltage and the current. One such device is the semiconducting circuit element known as a diode. A diode is a circuit device that allows current flow in only one direction. A diagram of a simple circuit consisting of a battery, a diode, and a resistor is shown in Figure 9.21 . Although we do not cover the theory of the diode in this section, the diode can be tested to see if it is an ohmic or a nonohmic device.

A plot of current versus voltage is shown in Figure 9.22 . Note that the behavior of the diode is shown as current versus voltage, whereas the resistor operation was shown as voltage versus current. A diode consists of an anode and a cathode. When the anode is at a negative potential and the cathode is at a positive potential, as shown in part (a), the diode is said to have reverse bias. With reverse bias, the diode has an extremely large resistance and there is very little current flow—essentially zero current—through the diode and the resistor. As the voltage applied to the circuit increases, the current remains essentially zero, until the voltage reaches the breakdown voltage and the diode conducts current, as shown in Figure 9.22 . When the battery and the potential across the diode are reversed, making the anode positive and the cathode negative, the diode conducts and current flows through the diode if the voltage is greater than 0.7 V. The resistance of the diode is close to zero. (This is the reason for the resistor in the circuit; if it were not there, the current would become very large.) You can see from the graph in Figure 9.22 that the voltage and the current do not have a linear relationship. Thus, the diode is an example of a nonohmic device.

Ohm’s law is commonly stated as V = I R V = I R , but originally it was stated as a microscopic view, in terms of the current density, the conductivity, and the electrical field. This microscopic view suggests the proportionality V ∝ I V ∝ I comes from the drift velocity of the free electrons in the metal that results from an applied electrical field. As stated earlier, the current density is proportional to the applied electrical field. The reformulation of Ohm’s law is credited to Gustav Kirchhoff, whose name we will see again in the next chapter.

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• Lab Explained: Ohm’s Law Lab

Research question:

How will increasing the voltage (v) to 5v, 10v, 20v, 35v, and then 50v affect the amount of current (Amps) measured by an ammeter, keeping the resistance (ohms) at 12 ohms and the wire length of 10cm constant, in a series circuit to prove ohms law?

Background information on Ohm’s law:

Ohms law can be used to identify the relationship between voltage, current, and resistance in any DC electrical circuit discovered by a German physicist named, Georg Ohm. This law states that voltage is equal to the product of the total current and the total resistance.

The equation for this law is often presented in a triangle where the voltage is on the top, current and resistance are on the bottom with only a line separating them;

In order to find the voltage, you must multiply the current and the resistance, to find the current or the resistance you must divide the voltage by either current (to find resistance) or resistance (to find current).

Hypothesis:

I predict that the higher the voltage, the higher the amount of current will be. I think this because there will be more power distributed throughout the series circuit due to the fact of a higher voltage, indicating that the current would run at a faster pace even with the resistance of 12 ohms.

If the voltage is 5 and the resistance is 12 ohms, the current would move at a slower pace and would decrease because the resistance causes that slower pace as a result of using more energy from the battery/voltage.

Independent variable: The independent variable is the amount of voltage; 5V, 10V, 20V, 35V, and 50V. Dependent variable: The dependent variable is the amount of current that is flowing in a series circuit measured in AMPS or A.

Controlled variable:

• Resistor X1
• Wires X7 (use more if needed)
• Switch X1 (optional, I didn’t use one as it is not mandatory)

When undertaking this experiment make sure to take safety precautions to be on the safe side and avoid any danger. Firstly, do not have any liquids around the circuit because if it spills it can cause major issues to the circuit such as creating sparks and or start possibly a fire, this is because liquids increase the conductivity of the electrical flow.

Ensure that all loose articles are not hanging from any place in your body like a tie, and if you have long hair tie it back so nothing is touching the circuit as it can irritate you and can be dangerous.

Lastly, check all the materials are in perfect condition to avoid any dangers that could happen, especially check the battery because if it’s not in perfect condition it can explode and become very harmful. 

Results Table:

Experiment conclusion:

The data shows that the higher the voltage, then the higher current, meaning that the voltage is directly proportional to the current, which is what ohms law states. This means When the voltage increases the current will always increase as long as there is no resistance or if the resistance stays the same.

For example, in my experiment, I increased the voltage from 5v,10v,20v,35v, to 50v while keeping the resistance the same so the current increased every time the voltage increased.

The law was proven for every trial I performed and this can be shown when dividing the voltage by the current to get the resistance. My hypothesis was correct, in my hypothesis, I claimed that the higher the voltage, the higher the current. As shown above, the voltage is directly proportional to the current.

One example from my results is when I increased the voltage to 50v I then divided that number by the current which was 4.17 to give me the amount of resistance which is 12ohms.

Experiment evaluation:

The overall experiment went well, and it succeeded the purpose of the trial which was how changing the voltage could affect the amount of current flowing in a series circuit while being able to prove ohms law. A weakness in my experiment is my graph of the results.

My graph was my weakness in this experiment because the graph should have mentioned the resistance as it is a key fact of proving ohms law.

One improvement I could have done to make the experiment better and get more accurate results was if I had added a voltammeter to the series circuit.

A voltammeter would read the amount of voltage that is given out of the battery used, therefore if I used a voltammeter, I could have ensured that the amount of voltage that was given out of the battery was correct and the results would be more accurate.

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Class 10 Physics (India)

Course: class 10 physics (india)   >   unit 3.

• Ohm's law
• Solved example: Ohms law
• Ohm's law and resistance

Ohm's law graph (verifying Ohm's law)

• Solved example: (Ohm's law graph)

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Video transcript

• Electricity
• Active page

Electricity of Class 10

The flow of electric current through a conductor depends on the potential difference across its ends. At a particular temperature, the strength of current flowing through it is directly proportional to the potential difference across its ends. This is known as Ohm's Law.

or V ∝ I V = Potential difference

V = RI R = Resistance

or R = V/I, I = Current

Here, R is the constant of proportionality, which depends on size, nature of material and temperature. R is called the electrical resistance or resistance of the conductor.

EXPERIMENTAL VERIFICATION OF OHM'S LAW

• Set up a circuit as shown in figure consisting of a nichrome wire XY of length, say 0.5 m, an ammeter, a voltmeter and four cells of 1.5 V each. (Nichrome is an alloy of nickel, chromium, manganese, and iron metal.)
• First use only one cell as the source in the circuit. Note the reading in the ammeter I, for the current and reading of the voltmeter V for the potential difference across the nichrome wire XY in the circuit. Tabulate them.
• Next connect two cells in the circuit and note the respective readings of the ammeter and voltmeter for the values of current through the nichrome wire and potential difference across the nichrome wire.

•  Repeat the above steps using three cells and then four cells in the circuit separately.
• Calculate the ratio of V to I for each pair of potential difference (V) and current (I).
• Plot a graph between V and I, and observe the nature of the graph.

Thus, V/I  is a constant ratio which is called resistance (R). It is known as Ohm’s Law.

RESISTANCE OF A CONDUCTOR:

The electric current is a flow of electrons through a conductor. When the electrons move from one part of the conductor to the other part, they collide with other electrons and with the atoms and ions present in the body of the conductor. Due to these collisions, there is some obstruction or opposition to the flow of electrons through the conductor.

The property of a conductor due to which it opposes the flow of current through it, is called resistance. The resistance of a conductor is numerically equal to the ratio of potential difference across its ends to the current flowing through it.

Resistance = Potential difference/Current, Or R = V/I

UNIT OF RESISTANCE

The S.I. unit of resistance is Ohm (Ω)

1 Ohm (Ω) = 1 volt(1V)/ Ampere(1 A)

The resistance of a conductor is said to be one ohm if a current of one ampere flows through it when a potential difference of one volt is applied across its ends.

CONDUCTORS, RESISTORS AND INSULATORS:

On the basis of their electrical resistance, all the substances can be divided into three groups:

conductors, resistors and insulators.

Conductors:

Those substances which have very low electrical resistance are called conductors. A conductor allows the electricity to flow through it easily. Silver metal is the best conductor of electricity Copper and Aluminium metals are also good conductors. Electric wires are made of Copper or Aluminium because they have very low electrical resistance.

Those substances which have comparatively high electrical resistance, are called resistors. The alloys like nichrome, manganin and constantan (or ureka), all have quite high resistances, so they are used to make those electrical devices where high resistance is required. A resistor reduces the current in the circuit.

Insulators:

Those substances which have infinitely high electrical resistance are called insulators. An insulator does not allow electricity to flow through it. Rubber is an excellent insulator. Electricians wear rubber handgloves while working with electricity because rubber is an insulator and protects them from electric shocks. Wood is also a good insulator.

CAUSE OF RESISTANCE:

There are many free electrons in a conductor. They move randomly when no electric current is passing through it. But when current is passed through it, they being negatively charged, start moving towards positive end of conductor, with a velocity called Drift velocity. During this movement, they collide with atoms, or ions of the conductor and thus their velocity is slowed down. This slow down due to obstruction is called Resistance.

Activity to show that the amount of current through an electric component depends upon its resistance:

•  Take a nichrome wire, a torch bulb, a 10 W bulb and an ammeter (0-5 A range), a plug key and some connecting wires.
•  Set up the circuit by connecting four dry cells of 1.5 V each in series with the ammeter leaving a gap XY in the circuit, as shown in figure.

•  Complete the circuit by connecting the nichrome wire in the gap XY. Plug the key. Note down the ammeter reading. Take out the key from the plug. [Note: Always take out the key from the plug after measuring the current through the circuit.]
•  Replace the nichrome wire with the torch bulb in the circuit and find the current through it by measuring the reading of the ammeter.
• Now repeat the above step with 10 W bulb in the gap XY.
•  You will notice that the ammeter readings differ for different components connected in the gap XY.
• You may repeat this Activity by keeping any material component in the gap. Observe the ammeter readings in each case. Analyse the observations.

Thus, we come to a conclusion that current through an electric component depends upon its resistance.

FACTORS AFFECTING RESISTANCE OF A CONDUCTOR

Resistance depends upon the following factors:-

(i) Length of the conductor.

(ii) Area of cross-section of the conductor (or thickness of the conductor).

(iii) Nature of the material of the conductor.

(iv) Temperature of the conductor.

Mathematically: It has been found by experiments that:

(i) The resistance of a given conductor is directly proportional to its length i.e.

R ∝ l ….(i)

(ii) The resistance of a given conductor is inversely proportional to its area of cross-section i.e.

R  ∝ 1/A  ….(ii)

From (i) and (ii), R  ∝ 1/A

R = ρ x 1/A…(iii)

Where ρ (rho) is a constant known as resistivity of the material of the conductor. Resistivity is also known as specific resistance.

DEPENDANCY OF RESISTANCE ON TEMPERATURE:

If R 0 is the resistance of the conductor at 0°C and R1 is the resistance of the conductor at t°C then the relation between R0 and R1 is given by,

R 1 = R o (1 + θαΔt) [Here Δt = t – 0 = t]

Here, a = Coefficient of Resistivity, t = temperature in °C

Experiment to show that resistance of a conductor depends on its length, cross section area and nature of its material.

• Complete an electric circuit consisting of a cell, an ammeter, a nichrome wire of length [marked (1)] and a plug key, as shown in figure.
• Now, plug the key. Note the current in the ammeter.

•  Replace the nichrome wire by another nichrome wire of same thickness but twice the length, that is 2 [marked (2) in the figure].
•  Note the ammeter reading.
•  Now replace the wire by a thicker nichrome wire, of the same length  [marked(3)]. A thicker wire has a larger cross-sectional area. Again note down the current through the circuit.
•  Instead of taking a nichrome wire, connect a copper wire [marked (4) in figure] in the circuit. Let the wire be of the same length and same area of cross-section as that of the first nichrome wire [marked(1)]. Note the value of the current.
•  Notice the difference in the current in all cases.
•  We notice that the current depends on the length of the conductor.
•  We also observed that the current depends on the area of cross-section of the wire used.

RESISTIVITY:

Resistivity,  ρ = R x A/1….(iv)

By using this formula, we will now obtain the definition of resistivity. Let us take a conductor having a unit area of cross-section of 1 m 2 and a unit length of 1 m. So, putting A= 1 and l = 1 in equation (iv),

Resistivity, ρ = R

The resistivity of a substance is numerically equal to the resistance of a rod of that substance which is 1 metre long and 1 metre square in cross-section.

Unit of resistivity,

The S.I. unit of resistivity is ohm-metre which is written in symbols as Ω - m.

Resistivity of a substance does not depend on its length or thickness. It depends only on the nature of the substance. The resistivity of a substance is its characteristic property. So, we can use the resistivity values to compare the resistances of two or more substances.

 Importance of resistivity:

A good conductor of electricity should have a low resistivity and a poor conductor of electricity should have a high resistivity. The resistivities of alloys are much more higher than those of the pure metals. It is due to their high resistivities that manganin and constantan alloys are used to make resistance wires used in electronic appliances to reduce the current in an electrical circuit.

Nichrome alloy is used for making the heating elements of electrical appliances like electric irons, room-heaters, water-heaters and toasters etc. because it has very high resistivity and it does not undergo oxidation (or burn) even when red-hot.

Effect of temperature on resistivity:

The resistivity of conductors (like metals) is very low. The resistivity of most of the metals increases with temperature. On the other hand, the resistivity of insulators like ebonite, glass and diamond is very high and does not changes with temperature. The resistivity of semi-conductors like silicon and germanium is in between those of conductors and insulators and decreases on increasing the temperature. Semi-conductors are proving to be of great practical importance because of their marked change in conducting properties with temperature and impurity concentration.

SPECIFIC USE OF SOME CONDUCTING MATERIALS:

Tungsten: It has high melting point of 3380ºC and emits light at 2127ºC. It is thus used as a filament in bulbs.

Nichrome: It has high resistivity and melting point. It is used as an element in heating devices.

Constantan and Manganin: They have modulated resistivity. Thus they are used for making resistances and rheostats.

Tin-lead Alloy: It has low resistivity and melting point. Thus it is used as fuse wire.

1. When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.

Solution: Given that voltage of battery V = 12 V

Circuit current I = 2.5 mA = 2.5 × 10 -3 A

∴ Value of resistance R =  V/I = 12/ 2.5 x 10 3 = 4800 Ω

2. Redraw the circuit of illustration 11, putting in an ammeter to measure the current through the resistors and a voltmeter to measure the potential difference across the 12 Ω resistors. What would be the readings in the ammeter and the voltmeter?

Solution: The redrawn circuit is shown in figure. Here, ammeter A has been joined in series of the circuit and voltmeter V is joined in parallel to 12 Ω resistors.

Here total voltage of battery V = 3 × 2 = 6 V

Total resistance R = R1 + R2 + R3 = 5 + 8 + 12 = 25 Ω

∴ Ammeter reading = Current flowing in the circuit I = V/R = 6V/25 = 0.24A

∴ Voltmeter reading = Potential difference across 12 Ω resistor

V ' = IR 3 = 0.24 × 12 = 2.88 V

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Ohms Law – Simon Ohms Amazing Experiment and Results

We all learn Ohms law from our elementary school. This a magical formula that solves most of the problems in electrical engineering. 

Did you know who is George Simon Ohm and how he created this amazing formula? We will explain it today.

Ohms Law Statement

This relationship states that: The potential difference (voltage) across an ideal conductor is proportional to the current through it. The constant of proportionality is called the “resistance”, R. 

Who is Georg Simon Ohm?

Georg Simon Ohm a German physicist investigated the relationship between current and voltage in a resistor and published his experimental results in 1827.

Ohms Experiment

For every voltage value, the current is recorded and the corresponding point is plotted on the rectangular graph.

Experiment Results

The experimental results indicate that there is a linear relationship between the current and voltage both in the first and third quadrant.

The equation explains ohm’s law which is stated as follows :

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Ohm’s law.

Experiment #22 from Physics with Vernier

Video Overview

Introduction

The fundamental relationship among the three important electrical quantities current , voltage , and resistance was discovered by Georg Simon Ohm. The relationship and the unit of electrical resistance were both named for him to commemorate this contribution to physics. One statement of Ohm’s law is that the current through a resistor is proportional to the potential difference, in volts, across the resistor. In this experiment, you will see if Ohm’s law is applicable to several different circuits using a Current Probe and a Differential Voltage Probe.

Current and potential difference, in volts, can be difficult to understand, because they cannot be observed directly. To clarify these terms, some people make the comparison between electrical circuits and water flowing in pipes. Here is a chart of the three electrical units we will study in this experiment.

• Determine the mathematical relationship between current, potential difference, and resistance in a simple circuit.
• Compare the potential vs. current behavior of a resistor to that of a light bulb.

Sensors and Equipment

This experiment features the following sensors and equipment. Additional equipment may be required.

Correlations

Teaching to an educational standard? This experiment supports the standards below.

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5 Error Sources in Ohm’s Law Experiment [How to avoid them]

The practical observations of  Ohm’s law experiment  never match the theoretical readings.

In fact, you can never match the theoretical calculations with practical values.

However, you can take some precautions to closely match the values.

Today’ you’ll learn the 5 error sources which are responsible for misleading readings. You’ll learn to keep you and your equipment safe by avoiding the blunders. You’ll also learn to obtain quite accurate readings. Let’s start off by understanding the types of errors.

Scientific measurement and instrumentation errors are often classified into three types:

• Personal errors: Mistakes made by the user due to his inexperience.
• Systematic: The faults in the instrument itself and the faults which may occur due to environmental conditions.
• Random errors: An accidental error whose cause is unknown. (We’ll ignore it here).

What is a personal error [Don’t of Ohm’s law]

Generally, a personal error is an outright mistake which is made by the person himself. For example, you ignore a digit while taking observations. In case of Ohm’s law, you can commit a personal error by:

Wrong connecting the circuit

The ammeter is used to measure the current.  It always connects in series with the circuit. Wrong connecting the ammeter will damage the instrument.

The voltmeter measures the potential difference between two points. It connects in parallel to the circuit. Wrong connecting the voltmeter will yield wrong readings.

Wrong taking the readings

Wrong measurements usually happen due to careless handling behavior. Carefully take the readings to avoid the errors.

Systematic errors

Tolerance values of resistors.

Carbon and metal film resistors are the most popular class of resistors which are employed in our labs. Such resistors have a tolerance value which ranges between 0.05-20%. The leftmost band of carbon resistors indicates the possible tolerance of resistance. A silver band indicates a tolerance of 10%, the golden band indicates 5% and brown band indicates 1%. More tolerance means your resistance, and thus the voltage/current will fluctuate away from the theoretical value.

You have two choices to bypass this error.

Use a brown [1%] or grey [0.05%] band resistor which has low tolerance value and thus will provide a lower error.

Measure the resistance first and base your theoretical formula calculations on this value.

Quality of Multimeter

Your multimeter is the actual tool which measures the electrical quantities. While low-quality multimeters yield wrong observations, they are equally dangerous. Again you have two choices.

Variable DC Power Supply

A variable power supply displays the output voltages on its main screen. For the time being, the accuracy of components decreases and your supply might display wrong results. Such cases are common in general labs where supplies are used thousands of times.

Use your multimeter to confirm the actual volts coming out of power supply.

Let’s summarize our results:

• ← Ohm’s Law in Series Circuits
• Theory VS Experimental Verification of Ohm’s Law →

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Experiment to Verify Ohm's Law

Last updated at April 16, 2024 by Teachoo

Graphical Representation Volt and Amperes

Experiment to Verify Ohm's Law

We take a conductor (Example Nichrome Wire)

We connect it to a circuit containing Voltmeter and Ammeter

When we supply current, we measure reading of Potential Difference with the help of Voltmeter and Electric Current with help of Ammeter

We calculate Ratio of Potential Difference/Electric Current

Now,we increase amount of current,

We again measure reading of Potential Difference and Electric Current and again Calculate Ratio

We note that Ratio Remains the Same

Hence Ohm's Law, which states that Ratio of Potential Difference and Electric Current Remains the same, is verified

Q1. The values of Current (I) flowing through a conductor for the corresponding values of potential difference (V) are given. Plot a graph between V and I.

From the above table

We can see that,

the ratio of 𝑉/𝐼 is always constant.

This gives resistance

The resistance is 25 in above case

Q2. The values of Current (I) flowing through a conductor for the corresponding values of potential difference (V) are given. Plot a graph between V and I.

the ratio of V/I is always  constant.

The resistance is 4 in above case

Q3. The values of Current (I) flowing through a conductor for the corresponding values of potential difference (V) are given. Plot a graph between V and I. Hence. find the resistance.

From the above table We can see that, the ratio of 𝑉/𝐼 is nearly constant. To find resistance, we find the mean of the resistances found. R = (3.2 + 3. 3 + 3.35 + 3.4 + 3.3)/5 R = 16.55/5 R = 3.31 Ω

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