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

In a single-phase AC circuit, the power consumed by load resistance $R_L$ for an excitation $V_s$ is measured using a wattmeter. The same wattmeter is connected in two different topologies, Topology-A and Topology-B, as shown in the figure. Different branch currents and voltage drops are also marked in the figure. Among the following options, the condition that ensures low error in the wattmeter reading for both the topologies is

Match the following sensors with their most suitable applications.

A 3½ digit digital voltmeter has a specified accuracy of $\pm (0.5\%+1)$. If it is used to measure 10V DC voltage, the error in the measurement would be
Note: Accuracy of the digital voltmeter is expressed as $\pm (\%\text{ of reading }+\text{ digit})$.

The circuit shown in Figure (a) can be represented using its equivalent T-model as shown in Figure (b). The values of the inductances $L_1$, $L_2$, and $L_3$ in the equivalent T-model are

Three parallel admittances $Y_a=-j0.2$ S, $Y_b=0.3$ S, and $Y_c=j0.4$ S connected in parallel with a voltage source $V_s=10\angle 45°$ V, draw a total current $I_s$ from the source. The currents flowing through each of these admittances are $I_a$, $I_b$, and $I_c$, respectively. Let $I=I_b+I_c$. The phase relation between $I$ and $I_s$ is