AC Voltage Controllers Questions and Answers

Answer: A

For an AC voltage controller with an RL load, the load impedance angle is

\[ \begin{aligned} \phi = \tan^{-1}\frac{X}{R} \\ &= \tan^{-1}\frac{10}{10} = 45^\circ \end{aligned} \]

The thyristor can be fired only when the supply voltage is positive across it, and when the firing angle \(\alpha\) is less than or equal to \(\phi\), the current in the load has not yet fallen to zero when the next thyristor is gated, so the conduction is continuous and the output voltage is the full sinusoid of the supply: the firing angle then has no effect and the output is not controllable.

So control is lost for \(0^\circ \le \alpha \le 45^\circ\), and for \(\alpha > \phi\) the output voltage falls with increasing \(\alpha\). The answer is option A.

Answer: D

The output is not controllable for \(0^{\circ} \lt \alpha \lt 45^{\circ}\).

With an RL load, the current in an ac voltage controller lags the voltage by the load angle \(\varphi\). If a thyristor is fired before \(\alpha = \varphi\), the other thyristor is still conducting, and the load simply receives the full sine wave, so changing \(\alpha\) in that range has no effect.

\[ \begin{aligned} \varphi &= \tan^{-1}\frac{X_{L}}{R} \\ &= \tan^{-1}\frac{50}{50} = 45^{\circ} \end{aligned} \]

So control is lost for \(0^{\circ} \lt \alpha \lt 45^{\circ}\), and the useful control range is \(45^{\circ} \le \alpha \le 180^{\circ}\). The other ranges all lie, at least partly, inside that controllable region.

Answer: D

Speed and torque are varied by stator voltage, rotor voltage and frequency control.

An induction motor's speed-torque characteristic can be changed in several ways: by varying the stator voltage (simple but with limited range), by injecting a voltage into the rotor circuit of a slip-ring motor (slip-power recovery and rotor resistance control), and by varying the supply frequency, usually with voltage in proportion (V/f control), which gives wide, efficient speed control with variable-frequency drives.

Chopper control and current control alone are only parts of particular schemes, and rotor voltage control alone applies only to slip-ring motors, so the option combining all three methods is the complete answer.