BY R OTATING V ECTORS — P HASORS In the previous section, we learnt that the current through a resistor is in phase with the ac voltage. But this is not so in the case of an inductor, a capacitor or a combination of these circuit elements. In order to show phase relationship between voltage and current in an ac circuit, we use the notion of phasors . The analysis of an ac circuit is facilitated by the use of a phasor diagram.
A phasor * is a vector which rotates about the origin with angular speed ω , as shown in Fig. . . The vertical components of phasors V and I represent the sinusoidally varying quantities v and i .
The magnitudes of phasors V and I represent the amplitudes or the peak values v m and i m of these oscillating quantities. Figure . (a) shows the voltage and current phasors and their relationship at time t for the case of an ac source connected to a resistor i.e., corresponding to the circuit shown in Fig. .
. The projection of voltage and current phasors on vertical axis, i.e., v m sin ω t and i m sin ω t , respectively represent the value of voltage and current at that instant. As they rotate with frequency ω , curves in Fig. .
(b) are generated. From Fig. . (a) we see that phasors V and I for the case of a resistor are in the same direction.
This is so for all times. This means that the phase angle between the voltage and the current is zero.