To Determine the Internal Resistance of a Given Primary Cell Using a Potentiometer Experiment

What is a Potentiometer and How to Measure Internal Resistance? 

A potentiometer is a three-terminal device that is used to determine the potential differences in a circuit by manually varying the resistances. With the help of a potentiometer, one can also find the internal resistance of a cell and the EMF between two cells. There are different types of potentiometers available such as rotary potentiometer, linear potentiometer etc. 


Internal Resistance in Potentiometer

In an electrical circuit, we use a device called a Potentiometer to measure the following things

  • To measure the internal resistance of the cell

  • To compare emf or the electromotive force between two cells

  • To measure the potential difference across a resistor


A potentiometer consists of a long wire of uniform cross-sectional area and a length of 10 metres provided that the wire should have high resistivity and a low-temperature coefficient.


In this article, we will perform an experiment to determine the internal resistance of a cell using the Potentiometer formula.


What is Internal Resistance?

If an electrical power source is a linear electric circuit, then according to Thévenin's theorem, it can be represented as an ideal voltage source in series with an impedance, and this impedance is called the internal resistance of the source.


How to Find Internal Resistance of a Cell Using a Potentiometer?

Now, let’s understand the theory on how to find the internal resistance of a cell using a potentiometer followed by the experiment on the determination of potential difference using a potentiometer.


Theory: We know that a potentiometer is used to determine the internal resistance of a cell. Besides this, we will have a determination of potential difference using a potentiometer.


The internal resistance of a cell using the potentiometer formula is given by:

r = (E/I - R)......(1)


And,


Determination of Potential Difference Using Potentiometer, the formula is:


E = I (R + r).....(2)


Here,


r = internal resistance of the cell in


E = electromotive force in Volts


I = current in amperes (amp)


R = Load resistance of the load in the circuit in


We know by Ohm’s law:


V = IR = E - Ir ….(3)


Equation (3) indicates that the value of V is less than E by an amount equal to the fall of potential inside the cell due to its internal resistance.


From equation (3), we have:


r/R = (E - V)/V


Therefore, the internal resistance of the cell is:


r  = R (E - V)/V  …..(4)


So, equation (4) is the Formula for Internal Resistance In Potentiometer.


To Determine the Internal Resistance of a Given Primary Cell Using a Potentiometer Experiment

The aim of our experiment is To Determine The Internal Resistance Of A Given Primary Cell Using A Potentiometer Experiment.


Materials required for the experiment:

  • A galvanometer

  • One battery

  • A potentiometer

  • A rheostat of low resistance

  • One fractional resistance box

  • One high resistance box

  • One ammeter

  • Two one-way number keys

  • Connecting wires

  • A jockey

  • Sandpaper

  • One Leclanche cell

  • One set square

  • A voltmeter


Below is the Circuit Diagram for the Potentiometer


(image will be uploaded soon)


Where the internal resistance of the cell can be determined by the following formula:


r  = (L1 - L2)/(L2) * R


Here,


L1 = a balancing length without a shunt resistance


L2 = a balancing length with a shunt resistance


Procedure to Perform the Experiment

  1. We must make sure that connections should be according to the diagram drawn above.

  2. Use sandpaper to clean the ends of the connecting wires and make sure that the connections are tight.

  3. Make sure that the plugs in the resistance box are tight.

  4. We must note that the e.m.f of the cell and battery is more than that of the cell. If it is not then we would not be able to obtain the null point.

  5. We can minimise rheostat resistance by taking maximum current from the battery.

  6. To check if the connections in the circuit are correct, the galvanometer deflections must be in the opposite direction. This is done by inserting the key K1 and making the note of the ammeter reading.

  7. To get the null point on the fourth wire, the rheostat should be adjusted/fixed without inserting the key K2.

  8. Take the small range resistance between 1-5 from resistance box R connected in parallel with the cell.

  9. Slide the jockey and get the null point.

  10. Finally, record your observations.


Our Observations on Determining the Internal Resistance in Potentiometer

Below are the calculations on determining the internal resistance in the potentiometer:

  • The least count or the L.C. of the voltmeter =.....

  • Range of voltmeters =.....

  • EMF of the cell =.....

  • EMF of a battery =......


Table for the measured lengths:


Corrected reading of ammeter (A)

Balance point when E1 (Leclanche cell) in the circuit L1

Balance point when E2 (Leclanche cell) in the circuit L2

(E1/E2) = (I1/I2)
























Internal Resistance Calculations

  1. For each set of observations find mean and L2.

  2. Then calculate the value of r for each set.

  3. Take the mean of obtained values of r.

 

Result Obtained

The value of the internal resistance is……..Ohms.


Precautions on Determination of Internal Resistance in Potentiometer

Precautions while performing the experiment:

  1. The e.m.f of the cell must be less than that of the battery.

  2. Keep an eye to make sure that the ammeter reading remains the same or constant at least for the first set of readings.

  3. Ensure that the current is passed only while obtaining the null point.

  4. Make sure that the rheostat should remain fixed.

  5. During the experiment, the cell should remain undisturbed.

  6. Make sure that the jockey should not be rubbed against the potentiometer wire.


Points to remember about potentiometer- 

  1. A three-terminal device with a variable resistance to control the flow of the current. 

  2. Used to determine the EMF, unknown voltage, and the internal resistance.

  3. Generally abbreviated as POT.

  4. The resistive wire used in a potentiometer is usually made up of metals such as manganese and constantan due to their properties by which there is not much variation in the resistance when the temperature changes. 

  5. A potentiometer is pocket-friendly, easy to use, and has high accuracy.

  6. Different types of potentiometers are available such as rotary potentiometers, linear potentiometers, digital potentiometers, mechanical potentiometers, etc. Rotary potentiometers are widely recognized and used. 

  7. The sensitivity of a potentiometer is directly proportional to the length of the resistance. Therefore, if the length of the potentiometer resistance then the resistance per unit voltage also increases. 


Conclusion 

This is how a potentiometer is used to calculate the internal resistance of a primary cell. Understand how the experiment is conducted to realize the use of a potentiometer and get the best results when you do it practically.

FAQs on To Determine the Internal Resistance of a Given Primary Cell Using a Potentiometer Experiment

1. State the Steps to Determine the Internal Resistance of the Potentiometer with an Example.

Below are the steps for determining the internal resistance of the potentiometer:

  • First: Ascertain the electromotive force.
    For example, the value of an electromotive force is 10 V.

  • Second: Determine the current.
    For example, we assume that the value of a current is 10 amps.

  • Third: Determine the load resistance.
    For example, the value of load resistance R is 20 ohms.

  • Finally, calculate the internal resistance.

 

Using the following formula, we find the internal resistance as: 

 

              r  = E/I - R 

 

Putting the value of E, I, and R in the above equation, we get:

 

 10/10 – 20 = - 19 ohms

2. State the Difference Between a Potentiometer and a Rheostat.

Below are differences between the potentiometer and a rheostat:

  • In the potentiometer, the output voltage is considered between fixed and sliding contact, while in rheostat, the variable resistance is obtained between the fixed and sliding terminals. 

  • The resistance of the potentiometer gets connected across the circuit, the resistance of the rheostat is connected in series with the circuit.

  • We can use a potentiometer as a three-terminal variable resistor, but a rheostat is a two-terminal variable resistor.

  • We can use the potentiometer as a rheostat but a rheostat cannot be used as a potentiometer.

  • Potentiometers are more often used to vary voltage, while rheostats are used to vary current.

3. What are the uses of a potentiometer?

Given below are some of the uses of a potentiometer:

  • Slide and rotary potentiometers are low-power potentiometers that are used as audio control devices. The faders in the sliding potentiometer and the knobs in the rotary potentiometers are used to set the frequency, adjust loudness, and other such characteristics of audio. 

  • Potentiometers can also be used in televisions for controlling the brightness of a picture, its contrast, etc.

  • The most basic use of a potentiometer is to measure the voltage. 

  • As we learned, it can also be used to find the EMF between two cells and also the internal resistance. 

  • A potentiometer can be used to ensure the correct position of a bridge or a walking ramp. They are also used for the precise measurements of angles.

4. What are the differences between a potentiometer and a voltmeter?

Potentiometers and Voltmeters, both are used to measure the voltage but they do have some key differences. Some of the major differences are given below-  

  • A potentiometer is a device used to measure an unknown voltage by comparing it to the known voltage whereas a voltmeter is used to determine the terminal voltage of a cell. 

  • A potentiometer can also determine the internal resistance and EMF but a voltmeter cannot determine either of them. 

  • The accuracy of a potentiometer is high whereas the accuracy of a voltmeter is less as compared to the former. 

  • A potentiometer is not portable but a voltmeter is a portable device.

  • One can directly get the reading from a voltmeter whereas a potentiometer does not give direct readings. 

  • A potentiometer has high sensitivity as compared to a voltmeter.

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