201.MET October 2022 Q.7(b)

 A battery-charging circuit is shown below in Fig. The forward resistance of the diode can be considered negligible and the reverse resistance infinite. The internal resistance of the battery is negligible. Calculate the necessary value of the variable resistance R so that the battery charging current is 1.0 A.

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Given

Vmax = 200 V

v = 100 V

I = 1 A

To find

Variable resistance , R

Solution

It is given that v = 200 sin ωt

                    100 = 200 sin ωt

                 sin ωt = 0.5

                       ωt = Sin-1 0.5

                            = 30 deg or 150 deg

                            = π/6 or 5(π/6)

Therefore diode conducts when ωt is between π/6 and 5(π/6)

Applying ohm's Law

I = V / R

1 = (200 sin ωt - 100) / R

Here I is the charging current  so to find average current we need to integrate the equation using the limits π/6 and 5(π/6)

Mean value of current = ∫ f dx