GATE EE 2020 Set 1 — Question 22

The two anti-parallel thyristors form a single-phase AC voltage controller feeding the load $Z = 10\angle -60^\circ\ \Omega$ from a $200\text{ V}$, $50\text{ Hz}$ source.Maximum power. With full conduction the whole source voltage appears across the load:$$I = \frac{200}{10} = 20\text{ A},\qquad R = 10\cos 60^\circ = 5\ \Omega,\qquad P_{max} = I^2R = 20^2 \times 5 = 2000\text{ W} = 2\text{ kW}$$Load angle. The impedance angle is printed as $-60^\circ$, i.e. a capacitive (R–C) load whose current leads the voltage. The usual firing-angle analysis of an AC voltage controller (full output for $\alpha \le \phi$, power falling to zero as $\alpha \to 180^\circ$) applies to a lagging (R–L) load. With an ideal capacitive load, firing a thyristor at a non-zero instantaneous voltage gives an impulsive capacitor-charging current, so the conduction pattern does not follow that analysis.If the load were read as $10\angle +60^\circ\ \Omega$ (R–L, $\phi = 60^\circ$), any $\alpha \le 60^\circ$ gives the same full output of 2 kW and the power falls to zero at $\alpha = 180^\circ$, giving the range $60^\circ$ to $180^\circ$. The circuit as printed (leading load) does not support a unique choice among the options, so the question has no unique correct option and every option is accepted.Answer: No unique answer — all options are accepted.