GATE 2022 BM – Question 19

Measurements and Control Systems · Bridges and Impedance Measurement · 1 mark · Multiple choice

For the balanced Owen bridge shown, find the unknown inductance Lₓ and resistance Rₓ.

$L_x=R_2R_3/C_3,\ R_x=R_2C_1/C_3$
$L_x=R_2R_3C_1,\ R_x=R_2C_1/C_3$
$L_x=R_2R_3C_1,\ R_x=R_2C_3/C_1$
$L_x=R_2R_3C_3,\ R_x=R_2C_1C_3$

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Correct answer: (B) $L_x=R_2R_3C_1,\ R_x=R_2C_1/C_3$

Explanation

At balance the arm ratios satisfy (Rₓ+jωLₓ)/R₂=(R₃+1/(jωC₃))/(1/(jωC₁)). Expanding the right side gives C₁/C₃+jωR₃C₁. Equate real and imaginary terms: Rₓ=R₂C₁/C₃ and Lₓ=R₂R₃C₁. Thus B.

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