## Reactance

**Inductive
Reactance**

The inductive reactance X_{L}** of an inductance L at angular
frequency **
**w****
and frequency f is:
**X

_{L}

**=**

**w**

**L = 2**

**p**

**fL**

**For
a sinusoidal current i of amplitude I and angular frequency **
**w**:

**i = I sin****w****t**

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

**w**

**LI**

**cos**

**w**

**t = X**

_{L}

**I cos**

**w**

**t**

**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 /**

**w**

**C = 1 / 2**

**p**

**fC**

**For
a sinusoidal voltage v of amplitude V and angular frequency **
**w**:

**v = V sin****w****t**

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

**i = C dv/dt =**

**w**

**CV**

**cos**

**w**

**t = V**

**cos**

**w**

**t / X**

_{C}

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

** **