GATE 2024 IN – Question 56
A shielded cable with $C_{stray}=20$ pF and $R_{wire}=10$ Ω connects the inductive sensors shown. The RMS value of $V_{out}$ is ______ V (two decimal places). All components are ideal, and the sensors are not magnetically coupled.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2.81 to 2.85
Explanation
The ideal buffer drives the shield to the signal potential, eliminating current through stray capacitance. Infinite input impedance eliminates wire-resistance drop. The inductive divider voltage is $(L_2V_{s1}+L_1V_{s2})/(L_1+L_2)=2\sin(2000\pi t)$ V. The final amplifier gain is 2, giving peak 4 V and RMS $4/\sqrt2=\boxed{2.83}$ V.