The Maxwell bridge shown in figure is at balance. The parameters of Inductive coil are :
RSMSSB JE - 2025, RSMSSB - 2025,
Answer: D
The coil parameters are \(R = R_{2}R_{3}/R_{4}\) and \(L = C_{4}R_{2}R_{3}\).
At balance the products of opposite arms are equal. The coil is opposite the parallel \(R_{4}C_{4}\) arm, whose admittance is \(\frac{1}{R_{4}} + j\omega C_{4}\), and \(R_{2}\) is opposite \(R_{3}\):
\[ \begin{aligned} (R + j\omega L) &= R_{2}R_{3}\left(\frac{1}{R_{4}} + j\omega C_{4}\right) \\ &= \frac{R_{2}R_{3}}{R_{4}} + j\omega C_{4}R_{2}R_{3} \end{aligned} \]
Equating real parts gives \(R = R_{2}R_{3}/R_{4}\), and equating imaginary parts gives \(L = C_{4}R_{2}R_{3}\). Balance is independent of frequency, which is the bridge's advantage. The first option swaps the two results, and the options with \(R_{4}/R_{2}R_{3}\) or \(1/(C_{4}R_{2}R_{3})\) invert them.
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