How Does Power Balance in a Driven RLC Circuit?

[thelonious]

Homework Statement

For a driven RLC circuit, compare the power delivered by the source to the power dissipated as heat in the resistor.

Homework Equations

P$_{avg}$ = I$_{rms}$*V$_{rms}$*cos($\phi$)

The Attempt at a Solution

My thinking was that the power dissipated in the resistor would be less than the power delivered by the source.

I thought so because in addition to the energy radiated as heat at the resistor, energy is either being stored or being released back into the circuit by the capacitor and inductor.

However, I was told that the power at the source equals the power dissipated as heat in the resistor. If all of the source energy is accounted for by the capacitor, what happened to the energy in the inductor and capacitor?

 

[gneill]

Homework Statement

For a driven RLC circuit, compare the power delivered by the source to the power dissipated as heat in the resistor.

Homework Equations

P$_{avg}$ = I$_{rms}$*V$_{rms}$*cos($\phi$)

The Attempt at a Solution

My thinking was that the power dissipated in the resistor would be less than the power delivered by the source.

I thought so because in addition to the energy radiated as heat at the resistor, energy is either being stored or being released back into the circuit by the capacitor and inductor.

However, I was told that the power at the source equals the power dissipated as heat in the resistor. If all of the source energy is accounted for by the capacitor, what happened to the energy in the inductor and capacitor?

The inductor and capacitor are going to trade stored energy back and forth, true, but that energy is not manufactured by those components. Further, there are losses on every cycle in the resistance. The source has to replenish this energy if the circuit is to operate at a steady state.