# 1. RL Circuit Censider the following circuit, with an ideal battery with an EMF of 6, three resistors, and an inductor. Before t = O, the switch has

1. RL Circuit Censider the following circuit, with an ideal battery with an EMF of 6, three resistors, and aninductor. Before t = O, the switch has been open for a long time. At t = 0, the switch is closed. S R 2R (a) What are the currents 11,0 and I10 immediately after the switch is closed at t = 0?(b) What is the rate of change of 12 immediately after the switch is closed at t = 0? (c) What are the currents 11,00 and 12,00 and the energy stored in the inductor a long timeafter the switch is closed, i.e. as t —> 00? (d) Apply Kirchhoﬁ’s laws to obtain two differential equations involving I1(t) and I2(t). (e) Let’s guess that both currents are of the form I (t) = 0c, — (Ioo —Io)e’t/T. Substitute theseforms into your differential equations to determine whether this guess is correct and, if so,the value of 1′. (f) After the switch has remained closed for a very long time, the switch is reopened. Whatare the currents 11 and 12 and the power supplied by the inductor immediately after theswitch is reopened?

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