Calculating the Potential Difference per Unit Length in a Potentiometer

In order to calculate the potential difference per unit length in a potentiometer, we need to consider the following information:

Given:
- Length of the wire (L) = 400 cm
- Resistance of the wire (R) = 10 ohm
- Electromotive force (EMF) of the cell (E) = 2 volts
- Negligible internal resistance of the cell

Formula:
The potential difference per unit length (V) in a potentiometer is given by the formula:
V = E * (R / L)

Solution:
Using the given values, we can calculate the potential difference per unit length as follows:

Step 1: Convert the length of the wire from centimeters to meters:
L = 400 cm = 4 meters

Step 2: Substitute the given values into the formula:
V = 2 * (10 / 4) = 2 * 2.5 = 5 volts

Therefore, the potential difference per unit length in the potentiometer is 5 volts.

Explanation:
The potentiometer consists of a wire that acts as a variable resistor. When a cell with an EMF of 2 volts is connected to the potentiometer, a potential difference is set up across the wire. The potential difference per unit length is directly proportional to the resistance of the wire.

In this case, the wire has a length of 4 meters and a resistance of 10 ohms. By applying the formula V = E * (R / L), we can calculate the potential difference per unit length. The result is 5 volts, indicating that for every meter of wire, there is a potential difference of 5 volts.

This potential difference is used to measure unknown emf or potential difference across a circuit element. By sliding a jockey along the wire and finding the position where the potential difference across the jockey is zero, the unknown potential difference can be determined.

Overall, the potential difference per unit length in a potentiometer is an important parameter for measuring and comparing electrical potentials in a circuit.

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