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  • A potentiometer is used to determine the internal resistance (r) of a cell. The balancing length for the cell is found to be 450 cm when no external resistance is connected. When an external resist

A potentiometer is used to determine the internal resistance (r) of a cell. The balancing length for the cell is found to be 450 cm when no external resistance is connected. When an external resistance of 6 ohms is connected in series with the cell, the balancing length becomes 300 cm. The potential difference per unit length of the potentiometer wire is 0.05 V/cm. Determine the internal resistance (r) of the cell.

Option: 1

6ohms


Option: 2

170ohms


Option: 3

200 ohms


Option: 4

20 ohms


Answers (1)

best_answer

The internal resistance (r) of the cell can be calculated using the formula:

r=\frac{\text { Potential Difference Across the Cell }}{\text { Current Flowing Through the Circuit }}

The potential difference across the cell can be found as the difference between the potential differences when no external resistance is connected and when the external resistance is connected:

Potential Difference Across the Cell = Potential Difference (No External Resistance)−Potential Difference

Given that the potential difference per unit length is 0.05 V/cm and the balancing lengths are 450 cm and 300 cm, we can calculate the potential differences:

Potential Difference (No External Resistance) = 0.05 V/cm × 450 cm = 22.5 V

Potential Difference (With External Resistance) = 0.05 V/cm × 300 cm = 15 V

Substituting these values:

Potential Difference Across the Cell = 22.5 V − 15 V = 7.5 V The current flowing through the circuit (I) can be calculated using Ohm’s law (V = IR), where V is the potential difference across the cell, and R is the external resistance:

I=\frac{V}{R}=\frac{7.5 \mathrm{~V}}{6 \Omega}=1.25 \mathrm{~A}

Finally, we can calculate the internal resistance (r) using the formula:

r=\frac{\text { Potential Difference Across the Cell }}{\text { Current Flowing Through the Circuit }}=\frac{7.5 \mathrm{~V}}{1.25 \mathrm{~A}}=6 \OmegaHence, the internal resistance (r) of the cell is 6 ohms. Therefore, the correct answer is A.

Posted by

Divya Prakash Singh

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