The circuit to the right consists of a battery of voltage V = 10 Volts, a resist

Question

The circuit to the right consists of a battery of voltage V = 10 Volts, a resistor of resistance 100 ohm, a capacitor of capacitance 0.1 mu F, an inductor of inductance .001 H and a switch, S. The circuit is initially open and the capacitor is uncharged. At time t-0 the switch is thrown to position a. Find the current through the resistor immediately after the switch is thrown to position a. After a long time the capacitor is fully charged. Find the energy ultimately stored on the capacitor. Suppose that the switch is then thrown to position b. How long will it take for the energy on the capacitor to be transferred to the inductor?

Explanation / Answer

a) current through resistor =   V/R

                                           = 10/100

                                           = 0.1 A

b) energy stored in capacitor = 1/2CV2

                                               = 1/2 * 0.1 * 10-6 * 10 * 10

                                                = 5 * 10-6 J

c)     Here, time taken =   pi * sqrt(LC)/2

                                    = 3.14 * sqrt(0.001 * 0.1 * 10-6)/2

                                    = 1.57 * 10-5 sec

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