a A half-wave rectifier with a filter capacitor has a 120 V rms,60 Hz ac source, and the power delivered to the load is 40 W. Assuming the diode to be ideal and the RC time constant is large compared to the period of the sine wave, i) sketch the output voltage, vo(t), ii) derive a formula for the average output voltage, Vo, and find its value, iii) determine the value of the filter capacitor, C, needed to keep the peak-to-peak ripple across the load to less than 0.5 V, iv) sketch the diode current.
[Note: The peak-to-peak ripple is approximately given by Vo ~ Vm/(fRC).]
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b) Next suppose we want a variable output voltage, Vo, which is achieved by replacing the diode with a SCR whose firing angle, , will be controlled. Assuming load resistance, R = 60 , i) sketch v.t), ii) derive a formula for Vo, as a function of the SCR firing angle, ot = , iii) determine the value of a needed to deliver 40 W to the load.