Suppose a small resistance R is added in series to the LC circuit of Problem 38.3. Assume that Q(t) has the form Q(t) = Q? (t) cos ?t, where Q?(t) is a slowly changing function that would be constant if there were no resistance and

was determined in Problem 38.3. Compute the energy stored in this circuit U(t) as a function of Q?(t) in the approximation that Q??? ?Q?. Then compute the average (over a cycle of oscillation) rate of energy loss in the resistor U?, also in terms of Q?. Combine these results to show that U?= ?R?U?/L and therefore U? = U₀e^?Rt/L, when R is small.

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w = 1/ VLC