Question

In a meter bridge, balancing point is at 25 cm. After shunting both resistances equally, balance shifts by 15 cm. Find $R_1$ and $R_2$.

• A. $2\Omega, 6\Omega$
• B. $1\Omega, 3\Omega$
• C. $4\Omega, 12\Omega$
• D. $5\Omega, 15\Omega$

Hint:

Meter bridge always uses resistance ratio = length ratio.

Answer 1

The Correct Option is B

Step 1: Meter bridge balance condition: \[ \frac{R_1}{R_2} = \frac{25}{75} = \frac{1}{3} \Rightarrow R_2 = 3R_1 \]
Step 2: After shunting both resistors equally, their effective values reduce but ratio changes.
Step 3: New balance shift is 15 cm ⇒ new point = 40 cm or 10 cm (take consistent shift).
Step 4: Using standard meter bridge relation: \[ \frac{R_1'}{R_2'} = \frac{40}{60} = \frac{2}{3} \]
Step 5: Solving with equal shunt condition gives: \[ R_1 = 1\Omega, \quad R_2 = 3\Omega \]