The inductive reactance XL of an inductance L at angular frequency w and frequency f is:
XL = wL = 2pfL
For 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 = XLI coswt
The current through an inductance lags the voltage across it by 90°.
The capacitive reactance XC of a capacitance C at angular frequency w and frequency f is:
XC = 1 / wC = 1 / 2pfC
For 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 / XC
The current through a capacitance leads the voltage across it by 90°.
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