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: Symmetry
Swapping the two resistances swaps the two lengths: if one length was $l$, it becomes $100 - l$.

Step 2: Find l
$\dfrac{l}{100 - l} = \dfrac{1}{3}$ gives $l = 25$ cm, so the new length is $75$ cm.

Step 3: Shift
$|100 - 2l| = |100 - 50| = 50$ cm.

Step 4: Answer
50 cm. The other options (25, 33.3, 75 cm) are single lengths and not the difference between the two positions.

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