Problem 5.9. Let us consider on RL electric circuit with resistance, R, and inductance, L, connected in series. Even though no average electromotive force (EMF) exists across the resistor, because of the discrete character of the electrons in the circuit and their random motion, a fluctuating EMF, (t), exists whose strength is determined by the temperature, T. This, in turn, induces a fluctuating current, I(t), in the circuit. The Langevin equation of motion for the current is

If the EMF is delta-correlated, (E(12) E(1)) = g(12-1) and ((t)) = 0, compute, g, and the current correlation function, ((I(12)(t)))r. Assume that the average magnetic energy in the inductor is L()=kBT and (0) = 0, where I(0) = 10.

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20 3 L dt dl(t) + RI(t) = {(t), Fig. 5.5. 20 3 Fig. 5.6.