Physics: An Introduction Chapter 24 -- Reference Tools & Resources

Chapter 24: Alternating Current Circuits
Reference Tools & Resources

Reference Tools & Resources

I. Key Terms and Phrases

alternating current (AC): a current whose direction alternates in a circuit.

in phase: two alternating quantities that reach their maxima and minima simultaneously oscillate in phase.

phasor: an arrow in an x-y coordinate system that rotates counterclockwise to represent alternating voltage or current.

root mean square (rms): the square root of the mean of a squared quantity.

capacitive reactance: the resistance-like behavior of a capacitor in an AC circuit.

inductive reactance: the resistance-like behavior of an inductor in an AC circuit.

impedance: the resistance-like behavior of an AC circuit that combines the effects of the resistance, capacitive reactance and inductive reactance.

RLC circuit: an AC circuit containing a resistor, capacitor, and inductor in series.

power factor: a multiplicative factor, cos f, that determines the power consumed through the resistor in an RLC circuit.

II. Important Equations

Name/Topic Equation Explanation
alternating voltages and currents V = V_maxsinwt
I = I_maxsinwt Equations representing sinusoidally varying voltage and current.

capacitive reactance The definition of the capacitive reactance.

inductive reactance X_L = wL The definition of the inductive reactance.

impedance The impedance of an RLC circuit.

phase angle The tangent of the phase angle allows us to calculate f for an RLC circuit.

AC voltage V_max = I_maxZ The expression similar to Ohm's law for an AC circuit.

natural frequency The natural frequency of LC oscillation that produces resonance in an RLC circuit.

Name/Topic	Equation	Explanation
alternating voltages and currents	V = V_maxsinwt I = I_maxsinwt	Equations representing sinusoidally varying voltage and current.
capacitive reactance		The definition of the capacitive reactance.
inductive reactance	X_L = wL	The definition of the inductive reactance.
impedance		The impedance of an RLC circuit.
phase angle		The tangent of the phase angle allows us to calculate f for an RLC circuit.
AC voltage	V_max = I_maxZ	The expression similar to Ohm's law for an AC circuit.
natural frequency		The natural frequency of LC oscillation that produces resonance in an RLC circuit.

III. Know Your Units

Quantity Dimension SI Unit
reactance and impedance (X_C, X_L, Z) [M][L²][A^-2][T^-3] W

Quantity	Dimension	SI Unit
reactance and impedance (X_C, X_L, Z)	[M][L²][A^-2][T^-3]	W

IV. Miscellaneous Tips

There is an old mnemonic that people sometimes use to remember the phase relationships between the current and the voltages across inductors and capacitors in AC circuits. The mnemonic is based on the phrase

ELI the ICE man

and the associations E for emf (or voltage), I for current, L for inductor, and C for capacitor.

The word ELI contains the letter L and, therefore, refers to the inductor. Notice that the E in ELI comes before the I which serves to remind you that the voltage across the inductor "comes before" (or leads) the current. The words ICE contains the letter C and, therefore, refers to the capacitor. Since the E in ICE comes after the I, this word reminds you that the voltage across the capacitor "comes after" (or lags) the current. If you find mnemonic devices such as this useful, then this is a good one to use.