Inductors in an AC Circuit

Kirchhoff’s loop rule

Inductors in an AC Circuit

for a sinusoidal applied voltage, the current in an inductor always lags behind the voltage across the inductor by 90° (one- quarter cycle in time).

Inductors in an AC Circuit

(a) Plots of the instantaneous current iL and instantaneous voltage ΔvL

across an inductor as functions of time. The current lags behind the voltage by 90°. (b) Phasor diagram for the inductive circuit, showing that the current lags behind the voltage by 90°.

Inductors in an AC Circuit

The inductive reactance:

That the instantaneous voltage across the inductor is

Capacitors in an AC Circuit

Kirchhoff’s loop rule

Capacitors in an AC Circuit

The circuit reaches its maximum value when cosωt=1:

The capacitive reactance:

The RLC Series Circuit

φ - is some phase angle between the current and the applied voltage

The current at all points in a series AC circuit has the same amplitude and phase.

The RLC Series Circuit

Using the phase relationships, we can express the instantaneous voltages across the three circuit elements as

where VR, VL, and VC are the maximum voltage values across the elements:

The instantaneous voltage v across the three elements equals the sum