Q.If an AC voltage $V = 240 \sin 314t$ is applied to an SCR HWR. If it has firing angle 30$^\circ$, determine $V_{dc}$ and $I_{dc}$ when load resistance of 25 $\Omega$ is connected.

A controlled rectifier replaces the diodes of an ordinary rectifier with thyristors, so the average DC output can be controlled. Because a thyristor turns on only when a gate pulse is applied and blocks forward voltage until then, delaying the turn-on instant — the firing angle $\alpha$ — controls how much of each half-cycle reaches the load.

RC triggering is the most common way to control thyristor power. An RC lag network produces a capacitor voltage that lags the supply; when it rises to the trigger level it supplies gate current and fires the SCR. Varying the resistance changes the phase-lag angle and hence the power delivered.

In the half-wave circuit the SCR conducts once per cycle, from $\alpha$ to $\pi$, giving

The full-wave version places one thyristor after a diode bridge, so both half-cycles are used:

$V_{dc} = \frac{V_m}{\pi}\left(1 + \cos\alpha\right),\qquad I_{dc} = \frac{V_{dc}}{R}$ …