Discussion
Find the range of firing angle for which the output voltage of the given AC voltage controller is not controllable.
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.
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