A resistor R (R = 0.4Q) and aninductor L (L = 0.08 H) are connectedas shown. Initially

Chapter 11, Problem 27

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A resistor R (R = 0.4Q) and aninductor L (L = 0.08 H) are connectedas shown. Initially, the switchis connected to point A and there is nocurrent in the circuit. At t = 0 theLswitch is moved from A to B, so that the resistor and the inductor are con- lnected to Vs ( Vs = 6 V), and currentstarts flowing in the circuit. The switch remains connected to B until the voltageon the resistor reaches 5 V. At that time (tBA) the switch is moved back toA.The current i in the circuit can be calculated from solving the differentialequations:.R L diz + - dt = vs during the time from t = 0 and until the time when theswitch is moved back to A.iR + L dt!:!:.t = 0 from the time when the switch is moved back to A and on.The voltage across the resistor, vR , at any time is given by vR = iR.(a) Derive an expression for the current i in terms of R, L, Vs, and t for0 t tBA by solving the first differential equation.(b) Substitute the values of R, L, and Vs in the solution fori, and determinethe time t BA when the voltage across the resistor reaches 5 V.(c) Derive an expression for the current i in terms of R, L, and t, for tBA t bysolving the second differential equation.(d) Make two plots (on the same page), one for vR versus t for 0 t tBA andthe other for vR versus t for tBA t 2tBA.