AC Impedance

Calculate the impedance, phase angle, power, power factor, voltage, and/or current in a RLC series circuit consisting of any combination of resistors, capacitors, and inductors.

Express total impedance in rectangular and polar forms,

Explain the relationship between resistance, reactance, and impedance as it relates to the rectangular form of total impedance,

Sketch an impedance triangle.
Voltage in an AC circuit is given by: \(V = V_{max}\ \sin \omega t\)
While calculating Impedance (equivalent of resistance in AC circuits)

Resistance is plotted on xaxis as it is, going towards right direction.

Inductance is calculated using the following formula and plotted vertically upwards. \[X_{L} = 2 \pi f L\]

Capacitance is calculated using the following formula and plotted vertically downwards. \[X_{C} = \frac{1}{2 \pi f C}\]
So, the combined effect of inductance and capacitance Reactance is plotted on yaxis by taking the difference of \(\displaystyle X_{L}\) and \(\displaystyle X_{C}\). \[X = X_L  X_C\] Impedance is calculated using Pythagoras theorem \[Z = \sqrt{R^{2} + (X_{L}  X_{C})^{2}}\]
Power angle \(\phi\) is the angle between Z and R. Power factor = cos\(\phi\).

For purely resistive circuit, \(\phi\) = 0 and power factor = 1.

For purely inductive circuit, \(\phi\) = 90 and power factor = 0.

For purely capacitive circuit, \(\phi\) = 90 and power factor = 0.