Ad = 0, the open switch in Figure P31.46 is thrown closed. We wish to find a symbolic expression for the current in the inductor for time t > 0. Let this current be called i and choose it to be downward in the inductor in Figure P31.46. Identify the current through R to the right, and the current downward through R2.
(a) Use Kirchhoff's junction rule to find the relation among the three currents.
(b) Use Kirchhoff's loop rule around the left loop to find another relationship.
(c) Use Kirchhoff's loop rule around the outer loop to find a third relationship.
(d) Eliminate i1 and i2 among the three equations and find an equation involving only the current i.
(e) Compare the equation in part (d) with Equation 31.6 in the text. Use this comparison to rewrite Equation 31 in the text for the situation in this problem and show that i(t) = [1 - e^(-2t/L)] where R' = R + R1 + R2.