P, Q, R and S are four wires of resistances 3, 3, 3 and 4Ω 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.

$12 \Omega$

For making the combination as a balanced wheatstone bridge the equivalent resistance across S must be 3$\Omega$.

$ \Rightarrow \frac{4R}{4+R} = 3 \Rightarrow 4R = 12 + 3R \Rightarrow R = 12\Omega$

The correct answer is Option (2) → $12 \Omega$