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GATE 2020 IN – Question 64

Measurements · Electrical bridges: Wheatstone, Kelvin, Maxwell, Anderson, Schering and Wien bridges for R, L, C and frequency, Q-meter, megohm measurement · 2 marks · Numerical answer

The Maxwell–Wien bridge shown balances when C₁ = 100 nF and R₁ = 100 kΩ. Its excitation is √2 cos(1000t) V. Find the coil Q factor.

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Correct answer: 10 to 10

Explanation

For the balanced Maxwell–Wien bridge with a parallel R₁–C₁ standard arm, coil parameters satisfy $L_x=R_2R_4C_1$ and $R_x=R_2R_4/R_1$. Hence $Q=\omega L_x/R_x=\omega R_1C_1$. With ω = 1000 rad/s, R₁ = $10^5$ Ω and C₁ = $10^{-7}$ F, Q = 10. The other bridge resistances cancel.

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