Discussion
Following Wheatstone bridge is balance when \(P_{AB} = 500\ \Omega\), \(Q_{BC} = 250\ \Omega\) and \(S_{AD} = 12\ \Omega\). Determine \(R_{DC}\).
Answer: A
R_DC is 6 Ω. A Wheatstone bridge is balanced when the ratio of the resistances in one arm equals the ratio in the other, so the products of opposite arms are equal. With P in AB and Q in BC, S in AD and R in DC:
\[ \frac{P_{AB}}{Q_{BC}} = \frac{S_{AD}}{R_{DC}} \]
\[ \frac{500}{250} = \frac{12}{R_{DC}} \]
\[ R_{DC} = 6\ \Omega \]
The value 24 Ω is what one gets by taking the ratio the wrong way round, and 12 Ω and 48 Ω do not satisfy the balance condition. The first option is correct.
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