Question

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

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

Answer 1

The Correct Option is A

To solve this problem, we need to understand the principle of a potentiometer. A potentiometer is used to measure the electromotive force (EMF) of a cell by balancing it against a known potential difference. The balancing length (or null point) of the wire in the potentiometer setup is proportional to the EMF of the cell connected.

Let's analyze the given data and solve step-by-step: 

1. The balance point for the first cell with an EMF of \(1.5\, V\) occurs at a wire length of \(36\, cm\). According to the principle of the potentiometer, the balance condition is given by: \(E_1 \propto L_1\), where \(E_1 = 1.5\, V\) and \(L_1 = 36\, cm\).
2. Now, if another cell with an EMF of \(2.5\, V\) replaces the first cell, we need to find the new balance length \(L_2\).
3. Using the direct proportionality \(\frac{E_1}{E_2} = \frac{L_1}{L_2}\), the equation can be rearranged to solve for \(L_2\): \(L_2 = \frac{E_2 \cdot L_1}{E_1}\).
4. Substitute the values: \(L_2 = \frac{2.5\, V \cdot 36\, cm}{1.5\, V} = \frac{90\, cm}{1.5}\).
5. This simplifies to: \(L_2 = 60\, cm\).

Therefore, the balance point for the second cell with an EMF of \(2.5\, V\) occurs at \(60\, cm\) of the wire.

The correct option is: 60 cm.