Key Concepts in Alternating Current Circuits

ac current

current that fluctuates sinusoidally with time at a fixed frequency

ac voltage

voltage that fluctuates sinusoidally with time at a fixed frequency

alternating current (ac)

flow of electric charge that periodically reverses direction

average power

time average of the instantaneous power over one cycle

bandwidth

range of angular frequencies over which the average power is greater than one-half the maximum value of the average power

capacitive reactance

opposition of a capacitor to a change in current

direct current (dc)

flow of electric charge in only one direction

impedance

ac analog to resistance in a dc circuit, which measures the combined effect of resistance, capacitive reactance, and inductive reactance

inductive reactance

opposition of an inductor to a change in current

phase angle

amount by which the voltage and current are out of phase with each other in a circuit

power factor

amount by which the power delivered in the circuit is less than the theoretical maximum of the circuit due to voltage and current being out of phase

quality factor

dimensionless quantity that describes the sharpness of the peak of the bandwidth; a high quality factor is a sharp or narrow resonance peak

resonant frequency

frequency at which the amplitude of the current is a maximum and the circuit would oscillate if not driven by a voltage source

rms current

root mean square of the current

rms voltage

root mean square of the voltage

step-down transformer

transformer that decreases voltage and increases current

step-up transformer

transformer that increases voltage and decreases current

transformer

device that transforms voltages from one value to another using induction

transformer equation

equation showing that the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of turns in their windings

AC voltage

v=V0sinωt

AC current

i=I0sinωt

capacitive reactance

V0I0=1ωC=XC

rms voltage

Vrms=V02√

rms current

Irms=I02√

inductive reactance

V0I0=ωL=XL

Phase angle of an RLC series circuit

ϕ=tan−1XL−XCR

AC version of Ohm's law

I0=V0Z

Impedance of an RLC series circuit

Z=R2+(XL−XC)2−−−−−−−−−−−−−−√

Average power associated with a circuit element

Pave=12I0V0cosϕ

Average power dissipated by a resistor

Pave=12I0V0=IrmsVrms=I2rmsR

Resonant angular frequency of a circuit

ω0=1LC−−−√

Quality factor of a circuit

Q=ω0Δω

Quality factor of a circuit in terms of the circuit parameters

Q=ω0LR

Transformer equation with voltage

VSVP=NSNP

Transformer equation with current

IS=NPNSIP