Discussion
In a single phase voltage controller circuit shown in figure below. For what range of triggering angle (α) the output voltage (Vo) is not controllable ?
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.
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