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.
6ohms
170ohms
200 ohms
20 ohms
The internal resistance (r) of the cell can be calculated using the formula:
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:
Finally, we can calculate the internal resistance (r) using the formula:
Hence, the internal resistance (r) of the cell is 6 ohms. Therefore, the correct answer is A.
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