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

To resolve this, the Wheatstone bridge must be balanced. Balance occurs when the resistance ratio in one arm equals the ratio in the other arm.

The given resistances are:

\(P = 3 Ω, Q = 3 Ω, R = 3 Ω, S = 4 Ω\)

The Wheatstone bridge balance condition is: \(\frac {P}{Q} = \frac {R}{(S_{parallel})}\)

We need to find the shunt resistance X, placed in parallel with S, that satisfies:

\(\frac {3}{3} = \frac {3}{4X/(4+X)}\)

This simplifies to:

\(1= \frac {3(4+X)}{4X}\)

\(4X = 3(4+X)\)

\(4X = 12 + 3X\)

Subtracting 3X from both sides yields:

\(X = 12\)

Therefore, the required shunt resistance to balance the bridge is \(12 Ω\).