#### A Resistor and a Capacitor

Place a resistor and capacitor in series with an AC source. What's the current?

If we had two resistors in series we'd add the individual resistances to find the equivalent resistance. We do the same thing here, only we add them *as vectors*, and we call the equivalent resistance the **impedance** of the circuit and give it the symbol Z.

Resistors want the voltage and current to be in phase, while capacitors want the voltage to lag behind the current by 90^{o}. When we add the resistances as vectors, then, the vectors are perpendicular.

Let's say we know the resistance R, capacitance C, and frequency f. To find the current follows these steps:

- Find the capacitive reactance of the capacitor: X
_{C} = 1/ωC, where ω = 2πf

- Find the impedance of the circuit: Z
^{2} = [R^{2} + X_{C}^{2}]

- Find the current from V = IZ.

- Find the phase angle from tan(φ) = -X
_{C}/R

The phase angle is the angle between the voltage and current in the circuit. This is stated as the voltage relative to the current, so the phase angle is positive if the voltage is ahead of the current and negative if the voltage lags the current.

#### A Resistor and an Inductor

Place a resistor and inductor in series with an AC source. What's the current?

Once again, to find the impedance (the equivalent resistance) we add the individual resistances as vectors. Resistors want the voltage and current to be in phase, while inductors want the voltage to lead the current by 90^{o}. Again the two vectors are perpendicular, with the effective resistance of the inductor in the opposite direction from the way the effective resistance of the capacitor went.

Let's say we know the resistance R, inductance L, and frequency f. To find the current follows these steps:

- Find the inductive reactance of the inductor: X
_{L} = ωL, where ω = 2πf

- Find the impedance of the circuit: Z
^{2} = [R^{2} + X_{L}^{2}]

- Find the current from V = IZ.

- Find the phase angle from tan(φ) = X
_{L}/R

#### Energy in an AC Circuit

Capacitors store energy in the electric field between the capacitor plates. In an AC circuit energy is continually being stored by the circuit and then given back to the circuit - none of the energy associated with the capacitor is lost.

Inductors store energy in the magnetic field. Here, too, energy is continually being stored and then returned to the circuit - none of the energy associated with the inductor is lost.

The components associated with energy loss in an AC circuit are the resistors.