Phase Relation in Pure Inductive Circuit

Phase Relation in Pure Inductive Circuit:

Phase Relation in Pure Inductive Circuit – As discussed already, the voltage current relation in the case of an inductor is given byPhase Relation in Pure Inductive Circuit

Consider the function i(t) = Im sin ωt = I[ Imejωt ] or Im∠0°

where

Vm = ωL Im = XLIm

ej90° = j = 1 ∠90°

If we draw the waveforms for both, voltage and current, as shown in Fig. 4.19, we can observe the phase difference between these two waveforms.

Phase Relation in Pure Inductive Circuit

As a result, in a pure inductor the voltage and current are out of phase. The current lags behind the voltage by 90° in a pure inductor as shown in Fig. 4.20.

Phase Relation in Pure Inductive Circuit

The impedance which is the ratio of exponential voltage to the corresponding current, is given by

Phase Relation in Pure Inductive Circuit

where

Vm = ωL Im

Phase Relation in Pure Inductive Circuit

where XL = ωL and is called the inductive reactance.

Hence, a pure inductor has an impedance whose value is ωL.

Phase Relation in Pure Capacitor:

As discussed already, the relation between voltage and current is given by

Consider the function i(t) = Im sin ωt = I[ Imejωt ] or Im∠0°

where

Vm = Im/ωC

Hence, the impedance is Z = -j/ωC = -jXC

Where XC = 1/ωC and is called the capacitive reactance.

If we draw the waveform for both, voltage and current, as shown in Fig. 4.21, there is a phase difference between these two waveforms..

Phase Relation in Pure Inductive Circuit

As a result, in a pure capacitor, the current leads the voltage by 90°. The impedance value of a pure capacitor

Phase Relation in Pure Inductive Circuit

Updated: April 27, 2020 — 10:36 am