Exercise 1 (RL circuit with a delay) In the figure below, R = 20, L = 6.0 H, the ideal battery has ε = 15 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) What is the current io at t = 0 in the inductor? (b) If the fuse has not blown, what can you say of the current in the resistor? (c) Use Kirchhoff's law to obtain a differential equation on i(t). Solve it and determine the time t at which the fuse blows. (d) Sketch a graph of the current I through the inductor as a function of time. Mark the time that which the fuse blows and the limit value of the current. Fuse 90 R L S

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