Electricity and Magnetism · Problem 7.15

ALTERNATING-CURRENT CIRCUITS — Edward Purcell & David Morin

Physics — E&M · rl-circuit-energy

Problem

Energy in an RL circuit * Consider the

RL

circuit discussed in Section 7.9. Show that the energy delivered by the battery up to an arbitrary time

t

equals the energy stored in the magnetic field plus the energy dissipated in the resistor. To do this, multiply Eq. (7.65) by

I

to obtain

I^2 R = I(\mathcal{E}_0 - L\,dI/dt)

, and then integrate this equation.