 In the Wheatstone bridge shown above, $P = 4\,\Omega$, $Q = 8\,\Omega$, $R = 6\,\Omega$. When the bridge is balanced ($i_g = 0$), find the unknown resistance $S$.
A$6\,\Omega$
B$12\,\Omega$
C$3\,\Omega$
D$9\,\Omega$
Answer & Solution
Correct answer: B. $12\,\Omega$
Wheatstone bridge **balance condition**: $\dfrac{P}{Q} = \dfrac{R}{S}$, which rearranges to $S = \dfrac{Q R}{P}$.
Substitute: $S = \dfrac{8 \times 6}{4} = 12\,\Omega$.
**Quick sanity check.** $P/Q = 4/8 = 1/2$ and $R/S = 6/12 = 1/2$ — equal ✓.
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