Question

P, Q, R, and S are four wires of resistances 3 Ω, 3 Ω, 3 Ω, and 4 Ω respectively. They are connected to form the four arms of a Wheatstone bridge circuit. The resistance with which S must be shunted in order that the bridge may be balanced is__________
Fill in the blank with the correct answer from the options given below.

• A. 14 Ω
• B. 7Ω
• C. 15 Ω
• D. 12 Ω

Answer 1

The Correct Option is D

Let's analyze the Wheatstone bridge and determine the shunt resistance.

1. Wheatstone Bridge Balance Condition:

For a Wheatstone bridge to be balanced, the ratio of resistances must be equal:

P/Q = R/S

2. Given Resistances:

• P = 3 Ω
• Q = 3 Ω
• R = 3 Ω
• S = 4 Ω

3. Shunting S:

Let the shunt resistance be X. When S is shunted with X, the effective resistance (S') becomes:

1/S' = 1/S + 1/X

1/S' = (X + S) / (SX)

S' = SX / (S + X)

4. Balanced Bridge with Shunted S:

For the bridge to be balanced:

P/Q = R/S'

3/3 = 3/S'

1 = 3/S'

S' = 3 Ω

5. Calculate Shunt Resistance (X):

We know S' = SX / (S + X) and S' = 3 Ω, S = 4 Ω:

3 = 4X / (4 + X)

3(4 + X) = 4X

12 + 3X = 4X

12 = 4X - 3X

X = 12 Ω

Therefore, the resistance with which S must be shunted is 12 Ω.

The correct answer is:

Option 4: 12 Ω