SOLUTION

Concept:

For controlling the load voltage, the minimum value of firing angle must be greater than the load phase angle.

That is, ${\alpha _{min}} > \varphi$

Where

$\varphi = {\tan ^{ – 1}}\left( {\frac{{\omega L}}{R}} \right)$

Therefore, firing angle for which the output voltage is uncontrollable is

$0 \le \alpha \le \varphi$

For controlling the load, the minimum value of firing angle α = load phase angle.

Phase angle φ = tan⁻¹(ωL/R)

φ = tan⁻¹(10/10) = 45°

The firing angle for which the output voltage is uncontrollable is

0 ≤ α_min ≤ φ

0° ≤ α ≤ 45°