Internal Resistance Of A Given Primary Cell Using Potentiometer Experiment

Potentiometer is a three-terminal resistor that uses sliding or rolling contact to produce an adjustable voltage divider. It comprises a long wire of uniform cross-sectional area and length such that the wire should have high resistivity and a low-temperature coefficient. The potentiometer can be used to determine the internal resistance of a primary cell. The internal resistance of a source is the impedance observed if an electrical power source is a linear electric circuit. According to Thévenin's theorem, such a power source can be represented as an ideal voltage source in series with an impedance, and this impedance is called the internal resistance of the source. This article discusses the experiment to determine the internal resistance of a primary cell using the potentiometer.

Key Takeaways: Potentiometer, Resistance, Primary cell, Internal resistance, Electromotive Force (e.m.f), Resistivity, Galvanometer, Ammeter, battery, Voltmeter

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Aim 

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The aim of this experiment is to determine internal resistance of a primary cell using a potentiometer.

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Materials Required 

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• 1 Galvanometer
• 1 ammeter
• 1 potentiometer
• 1 voltmeter
• 1 battery
• 1 rheostat of low resistance
• A fractional resistance box
• 2 numbers keys (one-way)
• Connecting wires
• A jockey
• 1 high resistance box
• Sandpaper
• 1 Leclanche cell
• 1 set square

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Theory

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The potentiometer is a device that is used to:

1. Measure the internal resistance of a cell 
2. Compare the e.m.f. of two cells
3. The potential difference across a resistor

The relation between potential difference, emf, and internal resistance of a cell is expressed by:

\(I = \frac{E}{R+r} \)

or

E = I(R+r)

Therefore,

V = IR = E - Ir

This shows that the value of V is less than E by an amount that is equal to the fall of potential inside the cell due to its internal resistance.

From the above equation:

\(\frac{r}{R} = \frac{E-V}{V} \)

Using a potentiometer, the internal resistance of a cell can be expressed as:

\(r = R\frac{E-V}{V} \)

Where,

r = internal resistance of the cell

E = electromotive force in Volts

I = current in amperes

R = Load resistance of the load in the circuit

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Circuit Diagram

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Here, the internal resistance can be estimated as r = (L₁ - L₂)/(L₂) * R

Where,

l₁ and l₂- balancing lengths without shunt or with the shunt.

R- shunt resistance in parallel with the given cell

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Procedure

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• Connect different electrical components according to the circuit diagram.
• Using sandpaper, clean the ends of the connecting wires and check the connections. All connections should be tight.
• Check the plugs in the resistance box. They should be tight.
• Check the e.m.f of the cell and battery. It should be more than that of the cell. If it is not then the null point would not be obtained.
• The rheostat resistance can be made minimum by taking maximum current from the battery.
• Check whether the circuit connections are correct. The galvanometer deflections should be in the opposite direction. Insert the key K1 and note the ammeter reading.
• To get the null point on the fourth wire, adjust the rheostat without inserting the key K2.
• Take a small resistance between 1-5 ohm from resistance box R connected in parallel with the cell.
• Slide the jockey and obtain the null point.
• Record the observations.

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Observations

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The least count of voltmeter = ………

Range of voltmeters = ……..

E.M.F of cell = ………

E.M.F of battery = ……

Table for lengths: 

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Calculations

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1. For each set of observations find mean and l₂
2. Calculate the value of r for each set.
3. Take the mean of values of r.

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Result

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The internal resistance of the given cell is …… Ohms.

Precautions

• The e.m.f of the cell should be less than the battery.
• Ensure that the ammeter reading remains constant at least for a single set of readings.
• The current should be passed only while obtaining the null point.
• The rheostat should remain fixed and the cell should remain undisturbed throughout the experiment.
• Do not rub the jockey against the potentiometer wire.

Sources of Error

• The wire of the potentiometer may not be of uniform cross-section.
• The brass strips at the ends may have a finite resistance. 
• Emf of the auxiliary battery producing the drop of potential along the wire may not remain constant throughout the experiment.
• The heating of the potentiometer wire by the current can also cause some errors.
• A zero error may occur in the measurement of l, due to the end of the scale not being exactly at the end of the wire.

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Things to Remember

• The potentiometer was first invented by Poggendorff. 
• The e.m.f of a cell is the potential difference across the terminals of the cell.
• A potentiometer works on the principle that for a constant current, the fall of potential in a wire is directly proportional to the length of the wire.
• Primary cells are those cells that cannot be recharged electrically i.e., the original state of the cell cannot be brought back by passing electrical energy from an external source. For e.g., Daniel Cell, Leclanche Cell, Manganese-alkaline cell, Mercury button cell.
• Secondary cells are those in which the chemical process is reversible and the original chemical state can be brought back supplying electrical energy through an external source. For e.g., alkali cells.

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