# hw09 - in parallel with the resistor as shown in the figure...

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Homework for Week 9: Due Thu April 7 in class 1. (“A RLC parts mystery.”) In this problem we are dealing with a series RLC circuit with unknown R, L, and C. The circuit shown in Fig. 1 has two identical capacitors, a resistor, and an inductor, connected to an AC emf with known 0 and . Two switches S1 and S2 can bypass the resistor and one of the capacitors. An oscilloscope (not shown) is connected to measure the full time dependence of the instantaneous current from the emf. The following measurements are available: i) With both switches open, the current leads the emf by 1 (where 1 >0). ii) With S 2 closed and S 1 still open, the emf leads the current by 2 (where 2 >0). iii) With both switches closed, the current amplitude is I. What are the values of R, C and L? 2. A capacitor is charged with an ideal battery of voltage V , disconnected, and then, at t = 0, connected to a circuit with an inductor L and resistor R connected in series. A fuse is connected
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Unformatted text preview: in parallel with the resistor, as shown in the figure. The fuse functions as a wire with no resistance until a current exceeds value Imax, after which it blows and then it acts an open connection. (a) At t = 0, what is the charge Q0, on the capacitor? What is the time dependence on the charge on the capacitor, Q(t), while the fuse is still intact. (b) What is the time depence on the current, I(t), while the fuse is still intact? (c) What is the maximal voltage of the emf, Vmax, for which the fuse will not blow? (d) [EXTRA CREDIT] Assume the voltage of the emf is barely enough for the fuse to blow. When will it happen? Explain in words what happens next to the charge on the capacitor and the current through the solenoid. Sketch Q(t+) where t+ is the time after the fuse has blown. [Hint: pay attention to the initial conditions at t+ = 0.]...
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