In the following circuit, the average voltage

$$ V_0=400\left(1+\frac{\cos \alpha}{3}\right) V $$

where $\alpha$ is the firing angle. If the power dissipated in the resistor is 64 W , then the closest value of $\alpha$ in degrees is

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a NewtonRaphson load-flow formulation, the UPS would be represented as a