# Electric Circuits

rename
Updated
2009-02-26 16:15

## Electric Circuits

Equation | Meaning |
---|---|

R_{eq}=R_{1}+R_{2} | equivalent resistance for 2 resistors in series |

R_{eq}=[(1/R_{1})+(1/R_{2})]^{-1}=(R _{1} R_{2})/(R_{1} + R_{2}) | equivalent resistance for 2 resistors in parallel |

L_{eq}=L_{1}+L_{2} | equivalent inductance for 2 inductors in series |

L_{eq}=[(1/L_{1})+(1/L_{2})]^{-1}=(L _{1} L_{2})/(L_{1} + L_{2}) | equivalent inductance for 2 inductors in parallel |

C_{eq}=[(1/C_{1})+(1/C_{2})]^{-1}=(C _{1} C_{2})/(C_{1} + C_{2}) | equivalent capacitance for 2 capacitors in series |

C_{eq}=C_{1}+C_{2} | equivalent capacitance for 2 capacitors in parallel |

V I | Power for a current I flowing through a potential drop V |

I^{2} R | Power lost for a current I flowing through a resistor R |

V^{2}/R | Power lost for a voltage V across a resistor R |

(1/2) Q V | Energy stored in a capacitor |

(1/2) Q^{2}/C | Energy stored in a capacitor |

(1/2) C V^{2} | Energy stored in a capacitor |

(1/2) L I^{2} | Energy stored in an inductor |

I R | Voltage drop across a resistor |

Q/C | Voltage drop across a capacitor |

L dI/dt | Voltage drop across an inductor |

dQ/dt | Current flowing through a capacitor |

C V | Charge stored on a capacitor |

0 | Total charge on an isolated piece of a circuit |

0 | Total current entering - Total current leaving a point in a circuit |

0 | Total voltage change for a loop in a circuit |

0 | Electric Field inside a conductor |

(ρ L)/A | Resistance of a piece of wire |

∞ | Resistance across a break in a circuit |

## AC Circuits

Equation | Meaning |
---|---|

i | sqrt(-1) |

1/i | -i |

1/(ωC) | reactance of a capacitor |

ωL | reactance of an inductor |

1/(iωC) | impedance of a capacitor |

iωL | impedance of an inductor |

R | impedance of a resistor |

V_{rms} | root mean squared voltage |

V_{o}/sqrt(2) | V_{rms} when V(t)=V_{o}sin(ωt) |

I_{rms} | root mean squared current |

I_{o}/sqrt(2) | I_{rms} when I(t)=I_{o}sin(ωt-φ) |

I_{rms}^{2} R = (1/2) I_{o}^{2} R | Average power dissipated by a resistor in an AC circuit |

V_{rms}^{2}/R = (1/2) V_{o}^{2}/R | Average power dissipated by a resistor in an AC circuit |

V_{rms} I_{rms} = (1/2) V_{o} I_{o} | Average power in an AC circuit |