Question

A metre bridge experiment, the resistance in the left gap is \(20 \Omega\) and in the right gap is \(60 \Omega\). The bridge is balanced. The distance of the null point from the centre of the wire is

• A. \(50\) cm
• B. \(75\) cm
• C. \(25\) cm
• D. \(40\) cm

Hint:

At balance, R1/R2 = l/(100 - l).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Metre bridge balance condition: \(\dfrac{R_{left}}{R_{right}} = \dfrac{l}{100 - l}\), where \(l\) is measured from the left end.

Step 2: Find the null point:
\[ \frac{20}{60} = \frac{l}{100 - l} \Rightarrow 60l = 20(100 - l) \Rightarrow 80l = 2000 \Rightarrow l = 25\ \text{cm} \]

Step 3: Distance from the centre:
The centre of the wire is at 50 cm. So the null point is \(50 - 25 = 25\) cm from the centre.

Step 4: Check:
Option (C). The value 25 cm from the left end happens to also be 25 cm from the centre in this case. Option (A) 50 cm and (B) 75 cm confuse the position with the position of the centre or the right end.

Final Answer:
Null point at 25 cm, which is 25 cm from the centre. \[ \boxed{\text{(C) }25\ \text{cm}} \]