GATE IN 2025 Question Paper (01-Feb-2025) (Shift 2)

In the circuit shown, the galvanometer (G) has an internal resistance of $100\Omega$. The galvanometer current $I_G$ is _________ $\mu A$ (rounded off to the nearest integer).

A series RLC circuit resonates at $7500rad/s$ for inductance $L=20mH$ and resistance $R=10\Omega$. The uncertainties in the measurement of $L$ and $R$ are $0.8mH$ and $0.3\Omega$, respectively. The percentage uncertainty in the measurement of quality factor is _________ $\%$ (rounded off to one decimal place).

In the circuit shown, the switch is opened at $t=0s$. The current $i(t)$ at $t=2ms$ is _________ $mA$ (rounded off to two decimal places).

A signal $V_M=5\sin (\pi t/3)V$ is applied to the circuit consisting of a switch S and capacitor $C=0.1\mu F$, as shown in the figure. The output $V_X$ of the circuit is fed to an ADC having an input impedance consisting of a $10M\Omega$ resistance in parallel with a $0.1\mu F$ capacitor. If S is opened at $t=0.5s$, the value of $V_X$ at $t=1.5s$ will be _________ $V$ (rounded off to two decimal places).
Note: Assume all components are ideal.

For the circuit shown in the figure, the active power supplied by the source is _________ $W$ (rounded off to one decimal place).