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AC Circuits Tip Sheet
The key to creating an AC circuit is an AC power supply. An AC power supply has two parameters, a
potential difference, E0, and a frequency or angular frequency, f or ω. An AC power supply can interact
with resistors, capacitors, inductors, and other circuit elements just like a DC battery or power supply.
Some equations from the DC circuit chapter can be retained while others must be discarded:
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Do not use Kirchoff’s voltage law or Kirchoff’s current law for mixed circuit elements.
Be careful calculating power (see below).
Do use formulas for equivalent resistance, capacitance, and inductance1 to simplify circuits.
Do assume that series circuit elements (regardless of type) have common currents and that
parallel circuit elements (regardless of type) have common potential differences.
Ohm’s Law
For capacitors and inductors in AC circuits, the concepts of “capacitive reactance” and “inductive
reactance” were invented so that they obey an equation like Ohm’s law. For more complex circuits, the
“impedance” can be calculated. Each formula for impedance only applies to that particular circuit.
Circuit
Resistor(s) only
Capacitor(s) only
Inductor(s) only
RC series3
RL series3
RLC series3
Name of Property
Resistance
Capacitive reactance
Inductive reactance
Impedance
Impedance
Impedance
Formula
R
Xc = 1/(ωC)
XL = ωL
Z = √(R2 + Xc2)
Z = √(R2 + XL2)
Z = √(R2 + (XL - Xc)2)
Ohm’s Law2
Vr = IR
Vc = IXc
VL = IXL
E0 = IZ
E0 = IZ
E0 = IZ
Power
Average power for resistors can be calculated with root mean squared (rms) values for current and
potential difference plus the formulas from the DC circuit chapter. Average power for capacitors and
inductors is zero. Average power for a single power supply is the sum of the powers of all the other
circuit elements.
Notation
AC currents and potential differences can be reported as maximum, rms, or instantaneous. Equations
for AC circuits typically use rms values, though maximum values can also be used. Instantaneous values
are not commonly considered. Since there are three ways to report these quantities, it is especially
important to use subscripts and distinguish between upper case (maximum or rms) and lower case
(instantaneous) in this chapter.
1 Multiple inductors use formulas similar to those of resistors. Inductors in series have equivalent inductance of L 1
+ L2 and inductors in parallel have equivalent inductance of (1/L1 + 1/L2)-1.
2 These formulas are valid for either maximum or rms, provided one is used exclusively.
3 Order does not matter here