Question

In a potentiometer circuit, a cell of EMF 1.5 V gives a balance point at 36 cm length of wire. If another cell of EMF 2.5V replaces the first cell, then at what length of the wire, the balance point occurs

• A. 62 cm
• B. 60 cm
• C. 21.6 cm
• D. 64 cm

Answer 1

The Correct Option is B

To solve this problem, we need to understand the working of a potentiometer. A potentiometer is a device used to measure the electromotive force (EMF) of a cell or to compare the EMF of two cells by balancing one EMF against the other.

The principle of potentiometer is that the potential drop across any part of the wire is directly proportional to the length of that part provided that the wire has uniform material and cross-section, and a constant current flows through it.

Let's denote:

• \(E_1 = 1.5 \, \text{V}\): EMF of the first cell
• \(L_1 = 36 \, \text{cm}\): Balance length for first cell
• \(E_2 = 2.5 \, \text{V}\): EMF of the second cell
• \(L_2\): Balance length for the second cell

The potentiometer principle states:

\(\frac{E_1}{E_2} = \frac{L_1}{L_2}\)

Substituting the given values:

\(\frac{1.5}{2.5} = \frac{36}{L_2}\)

Solving for \(L_2\), we have:

\(L_2 = \frac{36 \times 2.5}{1.5}\)

\(L_2 = \frac{90}{1.5}\)

\(L_2 = 60 \, \text{cm}\)

Therefore, the balance point for the second cell is at a length of 60 cm.

The correct answer is: 60 cm