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In a potentiometer circuit, if the balancing length is 50 cm for a cell of emf 1

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Question: In a potentiometer circuit, if the balancing length is 50 cm for a cell of emf 1.5V, what is the potential gradient if the total length of the wire is 100 cm?

Options:

  1. 3 V/m
  2. 1.5 V/m
  3. 0.75 V/m
  4. 2 V/m

Correct Answer: 0.75 V/m

Solution: 

The potential gradient is V/L = 1.5V/0.5m = 3 V/m, but since the total length is 1m, the gradient is 1.5 V/m.

In a potentiometer circuit, if the balancing length is 50 cm for a cell of emf 1

Practice Questions

Q1
In a potentiometer circuit, if the balancing length is 50 cm for a cell of emf 1.5V, what is the potential gradient if the total length of the wire is 100 cm?
  1. 3 V/m
  2. 1.5 V/m
  3. 0.75 V/m
  4. 2 V/m

Questions & Step-by-Step Solutions

In a potentiometer circuit, if the balancing length is 50 cm for a cell of emf 1.5V, what is the potential gradient if the total length of the wire is 100 cm?
  • Step 1: Understand that the balancing length of 50 cm means that the potential difference across this length is equal to the emf of the cell, which is 1.5V.
  • Step 2: Convert the balancing length from cm to meters. 50 cm is equal to 0.5 m.
  • Step 3: Calculate the potential gradient using the formula: Potential Gradient = Voltage / Length. Here, Voltage = 1.5V and Length = 0.5m.
  • Step 4: Substitute the values into the formula: Potential Gradient = 1.5V / 0.5m = 3 V/m.
  • Step 5: Note that the total length of the wire is 1m. Since the potential gradient is uniform, we need to find the potential gradient for the entire length of the wire.
  • Step 6: Since the total length is 1m, the potential gradient remains the same, but we express it as the total voltage over the total length: 1.5V / 1m = 1.5 V/m.
  • Potential Gradient – The potential gradient is the change in potential per unit length of the wire, calculated as the emf divided by the balancing length.
  • Balancing Length – The balancing length in a potentiometer is the length of the wire over which the potential difference is equal to the emf of the cell being measured.
  • Total Length of Wire – The total length of the wire in the potentiometer affects the calculation of the potential gradient, as it provides context for the distribution of potential along the wire.
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