Problem 62-3    Source:  Problem elaborated by the author of the site.

In a half-wave rectifier the capacitor value is 2 000 µF. The output voltage of the transformer secondary obeys the equation 20 sin 377ω. This circuit supplies a load of 62 Ω and which consumes a current of 0.29 A. Determine:

a) the value of the continuous voltage V_DC.

b) the peak-to-peak ripple value at the output.

c) what is the index or ripple factor.

Solution of the Problem 62-3   

Item a   

Since the secondary voltage was supplied in trigonometric form, the peak voltage, that is, V_p = 20  V. Therefore, to know the voltage across the capacitor, we must subtract the value of the voltage drop across the diode from this voltage. So the maximum voltage across the capacitor will be V_Cmax = 20 - 0.7 = 19.30  V . We also have ω = 377 rad/s, which results in f = 60 Hz. It is also reported that I_D = 0.29 A . With this data and using the eq. 62-02 , we can calculate V_DC , because

Item b   

Working algebraically in eq. 62-01, we find

Item c   

Using the eq. 62-04 , we have for the ripple factor

Carrying out the calculation, we found