GATE 2024 EE Q.23: solution and answer

Official answer: CSource: Official answer key, GATE 2024 EE (IISc Bengaluru)

1. How each is connected. A CT's primary is in series with the line. A PT's primary is connected in parallel across the grid, either line to line or line to neutral. So P goes with Y (PT). It cannot go with the CT.

2. CT primary current. The CT primary is in series with the line, so its primary current is simply the line current. The load on the system sets it, not the CT. So R goes with X (CT). A PT's primary current is only a small exciting current plus a reflected secondary current, not the line current.

3. CT with an open secondary. The primary current keeps flowing. With no secondary ampere-turns to oppose it, the whole primary MMF $N_1{I}_1$ magnetises the core. The flux rises and the core saturates, a dangerously high voltage appears across the secondary terminals, the core overheats, and it can keep residual magnetism. The secondary must therefore be kept short-circuited or loaded. So Q goes with X (CT). For a PT, an open secondary is close to its normal condition, because its burden is a high-impedance voltmeter or relay coil. So Q is not a PT feature.

4. PT primary current. A PT works like an ordinary power transformer fed from a fixed voltage. Its primary current is the phasor sum of the no-load (exciting) current and the secondary current reflected to the primary: ${\bar{I}}_1={\bar{I}}_0+\frac{{\bar{I}}_2}{n}$, where $n=N_1/N_2$ is the turns ratio. A larger secondary burden draws more $I_2$, so $I_1$ is larger. So S goes with Y (PT).

5. Why S is not a CT feature. In a CT the line fixes the primary current. Changing the burden changes the secondary voltage and the exciting current, which is where ratio and phase-angle errors come from, but it does not change $I_1$.

6. Result. X (CT): Q and R. Y (PT): P and S. This is option (C).