Double-Exponential LR Circuit
NAVAL ACADEMY ANNAPOLIS MD DEPT OF PHYSICS
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Simple LR and RC circuits are familiar to generations of physics students as examples of single-exponential growth and decay in the relevant voltages, currents, and charges. An element of novelty can be introduced by connecting two instead of one LR coils in parallel with a battery. The resulting circuit can still be treated using little more than the basic tools Kirchhoff s rules plus a trial exponential solution employed in the standard LR analysis. But the solution is now a double exponential, as can be verified by constructing such a circuit. Consider a circuit consisting of two inductors L1 and L2, one battery epsilon, one switch S, and three resistors R1 through R3. Assume the currents in the circuit have reached their steady-state values with switch S open. The switch is then closed at t 0. The problem is to find the subsequent currents in the circuit as a function of time.
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