Q:- Diagram shows a circuit for charging a 12 V battery. If v_s is a sinusoid along 24 V peak amplitude, search the fraction of each of cycle throughout which the diode conducts also search the peak value of the diode current & the highest reverse biases voltage that appears to the diode.

Solution :

The diode conducts while v_s exceed 12 V as indicated in the previous diagram. The conduction angle is 2θ, where θ is shown by

                                                24cosθ =12

                                                                cosθ = 1/2

                                                     θ = cos-1(1/2)

            Therefore θ= 60^o & the conduction angle is 120^o or one third of the cycle.

                        The peak value of the diode current is shown by

                                                  I_d = 24 - 12/100

                                                              = 0.12 A

            The highest reverse voltage across the diode occurs while v_s is at its negative peak and is equivalent to

                                                                        24 +12 =36 V