Question

Please show your work on how it is done. thank you!

1. An RL circuit comprised of one resistor and one inductor is shown in the figure below. The resistor and inductor are connected to a source of emf with negligible internal resistance by a switch a. The emf for this circuit is 12.0 V. The resistance of the resistor is 0.35 n, and the inductance of the inductor is 53 mH. For the circuit below Sketch the graph of current through the inductor as a function of time after the switch is closed to a a. b. Sketch the graph of the voltage across the inductor, E, as a function of time after the switch is closed to a. Please pay attention to the sign. What is the numerical value of the time constant for this eircuit? c. d. After the switch has been closed to a for an extended time, a student decides to close the switch to b (opening the switch a). Sketch the graph of current through the inductor as a function of time after the switch is moved to b. e. How much energy is stored in the magnetic field after the current has reached its maximum value? After how many time constants will the energy be 2 this maximum value?

Answer 1

telu Consider a series RL circuit where a resistor Rand inductor 1 Connected to a Source of emf & with negligible internal resistance eace by by Scott switch a Let i(t) be the current in the Circuit at any time t, Now, Kirchhoff's voltage law equations for the circuit Lo + Ri=E on integration, - 1 m (E-Ri) = + - + where, G is integration Constant At t=0, i=0 ,- 1 me

( (1-Pt) current through inductor, So, Graph time : of current through inductor as I tt 6 Now, wolt across the resistance R is UR = iR = e(1- eft) The voltage across the inductor & is & = E-vp = { eht

Graph & us time (6) Numerical value of time constant T = $3*10*5 = 0.1514285 T = 0.151428 Sec

R NOW, KVL equation becomes I di + Ri=0 di-dt om integration, e mi = - ht + (6 = constant) At t=0, is ek, Cza me So, current through inductor, 0.37 O TER
Thanks you.