Electricity and Magnetism · Problem 8.6

MAXWELL'S EQUATIONS AND ELECTROMAGNETIC WAVES — Edward Purcell & David Morin

Physics — E&M · limits-of-an-rlc-circuit

Problem

(a) In the

R \to 0

limit, verify that the solution in Eq. (8.4) correctly reduces to the solution for an

LC

circuit. That is, show that the voltage behaves like

\cos\omega_0 t

. (b) In the

L \to 0

limit, verify that the solution in Eq. (8.15) correctly reduces to the solution for an

RC

circuit. That is, show that the voltage behaves like

e^{-t/RC}

. You will need to use the results from Problem 8.4. (c) In the

C \to \infty

limit, verify that the solution in Eq. (8.15) correctly reduces to the solution for an

RL

circuit. That is, show that the voltage behaves like

e^{-(R/L)t}

, up to an additive constant. What is the physical meaning of this constant?