# Electric Circuits

Updated 2009-02-26 16:15

## Electric Circuits

EquationMeaning
Req=R1+R2equivalent resistance for 2 resistors in series
Req=[(1/R1)+(1/R2)]-1
=(R1 R2)/(R1 + R2)
equivalent resistance for 2 resistors in parallel
Leq=L1+L2equivalent inductance for 2 inductors in series
Leq=[(1/L1)+(1/L2)]-1
=(L1 L2)/(L1 + L2)
equivalent inductance for 2 inductors in parallel
Ceq=[(1/C1)+(1/C2)]-1
=(C1 C2)/(C1 + C2)
equivalent capacitance for 2 capacitors in series
Ceq=C1+C2equivalent capacitance for 2 capacitors in parallel
V I Power for a current I flowing
through a potential drop V
I2 RPower lost for a current I flowing
through a resistor R
V2/RPower lost for a voltage V
across a resistor R
(1/2) Q VEnergy stored in a capacitor
(1/2) Q2/CEnergy stored in a capacitor
(1/2) C V2Energy stored in a capacitor
(1/2) L I2Energy stored in an inductor
I RVoltage drop across a resistor
Q/CVoltage drop across a capacitor
L dI/dtVoltage drop across an inductor
dQ/dtCurrent flowing through a capacitor
C VCharge stored on a capacitor
0Total charge on an isolated piece of a circuit
0Total current entering - Total current leaving
a point in a circuit
0Total voltage change for a loop in a circuit
0Electric Field inside a conductor
(ρ L)/AResistance of a piece of wire
Resistance across a break in a circuit

## AC Circuits

EquationMeaning
isqrt(-1)
1/i-i
1/(ωC)reactance of a capacitor
ωLreactance of an inductor
1/(iωC)impedance of a capacitor
iωLimpedance of an inductor
Rimpedance of a resistor
Vrmsroot mean squared voltage
Vo/sqrt(2)Vrms when V(t)=Vosin(ωt)
Irmsroot mean squared current
Io/sqrt(2)Irms when I(t)=Iosin(ωt-φ)
Irms2 R = (1/2) Io2 RAverage power dissipated by a resistor in an AC circuit
Vrms2/R = (1/2) Vo2/RAverage power dissipated by a resistor in an AC circuit
Vrms Irms = (1/2) Vo IoAverage power in an AC circuit