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AimTo determine the internal resistance of a given primary cell using a potentiometer.
Apparatus Required1 galvanometer
A battery
1 potentiometer
1 rheostat of low resistance
A fractional resistance box
1 ammeter
2 numbers keys (one-way)
Connecting wires
A jockey
1 high resistance box
Sandpaper
1 Leclanche cell
1 set square
1 voltmeter
TheoryThe emf of a cell is the potential difference between its terminals when it is not connected to any external circuit. However, when a cell is connected to an external circuit, the potential difference between its terminals decreases due to its internal resistance.
To determine the internal resistance of a given primary cell, we can use a potentiometer. A potentiometer is a device that can be used to measure the potential difference between two points in an electrical circuit. In this experiment, a potentiometer is used to measure the potential difference between the terminals of the primary cell when it is connected to an external circuit.
Let E be the emf of the given primary cell, r be its internal resistance, V be the potential difference measured using the potentiometer, and R be the resistance of the potentiometer wire.
The potential gradient along the potentiometer wire is given by the equation:
φ = V / l
where l is the length of the wire between the zero end and the balancing point P.
At balance, the potential difference across the wire AB is equal to the emf of the cell, E.
Therefore, by applying the principle of Wheatstone’s bridge, we get:
E / V = R / (r + R)
From this equation, we can determine the internal resistance r of the given primary cell.
The potentiometer is a device utilized for measuring the internal resistance of a cell and for comparing the e.m.f. of two cells and the potential difference across a resistor. The relationship among potential difference, emf, and internal resistance of a cell can be expressed as:
V=IR = E-Ir
This implies that the value of V is less than E by an amount equivalent to the fall of potential inside the cell caused by its internal resistance. The internal resistance of the cell can be calculated from the equation:
r = [(R + r1) / R] * [(l1 / l2) – 1]
where l1 and l2 are the balancing lengths without or with the shunt, and R is the shunt resistance connected in parallel to the given cell.
ProcedureFollow the circuit diagram provided above when making the connections for this experiment.
Use sandpaper to clean the ends of the connecting wires and ensure that all connections are tight and secure.
Check that the plugs in the resistance box are tightly inserted.
Make sure that the e.m.f of the battery is greater than that of the cell, otherwise a null point cannot be obtained.
To minimize rheostat resistance, take maximum current from the battery.
Check that the galvanometer deflections are in the opposite direction by inserting key K1 and noting the ammeter reading.
To obtain the null point on the fourth wire, adjust the rheostat without inserting key K2.
Select a small resistance (between 1-5 ohm) from resistance box R and connect it in parallel with the cell.
Slide the jockey along the wire until a null point is obtained.
Record all observations made during the experiment.
Observation and ResultThe circuit diagram is set up as shown above.
The jockey is moved along the potentiometer wire until a null point is obtained.
The length of the wire from the zero end to the balancing point is noted as l.
The potential difference V across the balancing length of the potentiometer wire is measured using a voltmeter.
The experiment is repeated with different values of R to obtain multiple readings.
Result: The internal resistance r of the given primary cell can be calculated using the formula:
r = R[(l / V) – 1]
where R is the resistance of the potentiometer wire.
Calculation: For each reading, the value of r is calculated using the above formula. The average value of r is then calculated from the multiple readings to obtain the final value of the internal resistance of the given primary cell.