A delayed full-wave rectified sinusoidal current has an average value equal to half its maximum value. Find the delay angle θ.

Concept:

The average output voltage of a full-wave controlled rectifier with R load is given by:

\({V_0} = \frac{{{V_m}}}{\pi }\left( {1 + \cos \alpha } \right)\)

Where V_m is the maximum value of supply voltage

α is the firing angle or delay angle

Average load current:

\({I_0} = \frac{{{V_m}}}{{\pi R}}\left( {1 + \cos \alpha } \right) = \frac{{{I_m}}}{\pi }\left( {1 + \cos \alpha } \right)\)

Calculation:

Given that, the average value of the average load current is equal to half of its maximum value.

\(\frac{{{I_m}}}{2} = \frac{{{I_m}}}{\pi }\left( {1 + \cos \theta } \right)\)