Question

The total length of potentiometer wire AB is $50$ cm in the arrangement as shown in figure. If P is the point where the galvanometer shows zero reading then the length AP is _________ cm.

• A. 30
• B. 25
• C. 15
• D. 20

Hint:

In bridge balance problems, the ratio of the components on the left must equal the ratio of the components on the right.

Answer 1

The Correct Option is A

To solve the problem, we need to determine the point where the galvanometer shows zero deflection. This point is known as the null point in a potentiometer setup. In this condition, there is no potential difference across the galvanometer, and it reads zero.

1. The potentiometer wire AB has a total length of 50 \, \text{cm}.
2. In the setup shown, we have resistors of 6 \, \Omega and 4 \, \Omega in series across AB.
3. For the galvanometer to read zero, the potential drop across the length AP must be equal to the potential drop across the 6Ω resistor.
4. The total resistance of the resistors is 6 \, \Omega + 4 \, \Omega = 10 \, \Omega.
5. The potential across the 6Ω resistor is \(\frac{6}{10}\) of the total potential (V).
6. Since the wire is of uniform resistance, the length AP must be \(\frac{6}{10}\) of 50 cm, which gives: \text{AP} = \frac{6}{10} \times 50 = 30 \, \text{cm}

Thus, the length AP is 30 \, \text{cm}.

Therefore, the correct answer is 30 cm.