Halliday, Resnick & Walker — Induction and Inductance: Problem 75

75 In Fig. 30-56, \(R = 15 \ \Omega\), \(L = 15 \text{ H}\), the ideal battery has \(\mathcal{E} = 10 \text{ V}\), and the fuse in the upper branch is an ideal 3.0 A fuse. It has zero resistance as long as the current through it remains less than 3.0 A. If the current reaches 3.0 A, the fuse “blows” and thereafter has infinite resistance. Switch S is closed at time \(t = 0\). (a) When does the fuse blow? (Hint: Equation 30-41 does not apply. Rethink Eq. 30-39.) (b) Sketch a graph of the current \(i\) through the inductor as a function of time. Mark the time at which the fuse blows.