# AC circuit question

1. Dec 12, 2006

### johnboy14

Explain why a pure capacitor or a pure inductor does not consume electrical energy, while a pure resistor does. Illustrate your answer using waveform diagrams.

I need some wave diagrams for this. I have no idea what the waves look like

Last edited: Dec 12, 2006
2. Dec 12, 2006

### Staff: Mentor

For the inductor, draw the voltage and current waveforms versus time (assume sinusoidal excitation at some arbitrary frequency). What is the relationship between i(t) and v(t) for an inductor? What is the equation for the power consumed or supplied by an inductor? What is it net over a few periods of the sine wave?

Repeat for a capacitor and then a resistor. Show your work.

3. Dec 12, 2006

### chroot

Staff Emeritus
berkeman's post is excellent guidance, but I think I'll add a bit more detail.

Remember that reactive devices (like capacitors and inductors) have a phase shift between their V(t) and I(t) curves.

For example, the current through a capacitor is proportional to the time derivative of the voltage across it, correct?

$$I = C \frac{dV}{dt}$$

Well, that means if you put in a sine wave for V(t), I(t) must be a cosine wave -- a phase shift of ninety degrees.

Now, as berkeman says, find the instantaneous power consumed by the device by multiplying V(t) and I(t), and then integrate that over a period to find the average value.

- Warren