Question

The resistances in the two gaps of a balanced meter bridge are 'X' \(\Omega\) and '3X' \(\Omega\) respectively. If the resistances are interchanged the balance point shifts by

• A. \(25\) cm
• B. \(33.3\) cm
• C. \(50\) cm
• D. \(75\) cm

Hint:

At balance, the lengths are in the same ratio as the resistances; interchanging the resistances swaps the lengths.

Answer 1

The Correct Option is C

Step 1: Understand the concept
For a meter bridge, balance gives \(\dfrac{X}{3X} = \dfrac{l}{100 - l}\), with \(l\) measured from the end where \(X\) is connected.

Step 2: First balance point
\(\dfrac{1}{3} = \dfrac{l}{100 - l}\) gives \(100 - l = 3l\), so \(l = 25\) cm.

Step 3: After interchange
The ratio becomes \(\dfrac{3X}{X} = 3 = \dfrac{l'}{100 - l'}\), so \(l' = 300 - 3l'\) and \(l' = 75\) cm.

Step 4: Shift
The shift is \(75 - 25 = 50\) cm, option (C).

Final Answer:
The balance point shifts by 50 cm. This is option (C). \[ \boxed{\text{(C) }50\ \text{cm}} \]