Question

In a meter bridge, the balancing length from the left end (standard resistance of one ohm is in the right gap) is found to be 20 cm. The value of the unknown resistance is

• A. $0.8\, \Omega$
• B. $0.5\, \Omega$
• C. $0.4\, \Omega$
• D. $0.25\, \Omega$

Answer 1

The Correct Option is D

 To solve the problem of finding the unknown resistance in a meter bridge setup, we need to apply the concept of a Wheatstone bridge, as the meter bridge is based on it. Let's detail the solution step-by-step:

1. In a meter bridge, the formula used to find the unknown resistance is derived from the balancing condition of a Wheatstone bridge. The equation is given by:
   • \(R\): Unknown resistance in the left gap.
   • \(l_1\): Balancing length from the left end, which is given as 20 cm.
   • \(S\): Standard resistance in the right gap, which is 1 ohm.
2. Substitute the known values into the formula:
3. Simplify the fraction:

Hence, the value of the unknown resistance is \(0.25\, \Omega\).

In this problem:

• The given value of 20 cm is the balancing length from the left end.
• The meter bridge works on a 1-meter length, leading to the equation involving \((100 - l_1)\) for the right side.
• The options provided are evaluated in the context of the formula, confirming that \(0.25\, \Omega\) is correct.

Thus, the correct answer is \(0.25\, \Omega\), matching option \(0.25\, \Omega\).