### Formulas

*Inductive Reactance*

The inductive reactance **X _{L}** of an inductance

**L**at angular frequency

**w**and frequency

**f**is:

**X**

_{L}= wL = 2pfLFor a sinusoidal current **i** of amplitude **I** and angular frequency **w**:

**i = I sinwt**

If sinusoidal current **i** is passed through an inductance **L**, the voltage **e** across the inductance is:

**e = L di/dt = wLI coswt = X _{L}I coswt**

The current through an inductance lags the voltage across it by 90°.

*Capacitive Reactance*

The capacitive reactance **X _{C}** of a capacitance

**C**at angular frequency

**w**and frequency

**f**is:

**X**

_{C}= 1 / wC = 1 / 2pfCFor a sinusoidal voltage **v** of amplitude **V** and angular frequency **w**:

**v = V sinwt**

If sinusoidal voltage **v** is applied across a capacitance **C**, the current **i** through the capacitance is:

**i = C dv/dt = wCV coswt = V coswt / X _{C}**

The current through a capacitance leads the voltage across it by 90°.

NOTATION |
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susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power |
[siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] |
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quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency |
[number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec] |