GATE 2025 IN – Question 56
The shown AC bridge has $R=300\ \Omega$, $R_1=1000\ \Omega$, $R_2=500\ \Omega$, $L=30$ mH, and detector D. At balance, excitation frequency is ______ kHz (rounded to two decimal places).
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Correct answer: 1.55 to 1.65
Explanation
The upper-left impedance is $Z_1=R+j\omega L$; the upper-right is $Z_2=Rj\omega L/(R+j\omega L)$.
Balance requires $Z_1/Z_2=R_1/R_2=2$.
Expand: $(R+j\omega L)^2/(Rj\omega L)=2+j[\omega L/R-R/(\omega L)]$.
The imaginary part vanishes when $\omega L=R$.
Hence $f=R/(2\pi L)=300/(2\pi\times0.03)=1591.55\ldots$ Hz, or **1.59 kHz**.