**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 by

Consider the function **i(t) = I _{m} sin ωt = I_{m }[ I_{m}e^{jωt }] or I_{m}∠0°**

**where**

**V _{m} = ωL I_{m} = X_{L}I_{m}**

**e ^{j90° = 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.

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.

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

**where**

**V _{m} = ωL I_{m}**

where X_{L} = 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) = I _{m} sin ωt = I_{m }[ I_{m}e^{jωt }] or I_{m}∠0°**

**where**

**V _{m} = I_{m}/ωC**

Hence, the impedance is **Z = -j/ωC = -jX _{C}**

Where **X _{C} = 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..

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