 # Representation of AC current and voltage by phasor diagram

We have read about electrical circuits which contain a resistor connected across an AC source, an inductor connected across an AC source, a capacitor connected across an AC source or the combination of any two or all three of these components connected across an AC source. We know that, in the case of a resistor, the current across the resistor is in phase with the voltage source. But in the case of an inductor or a capacitor, the current either lags or leads the voltage source to a certain value. In order to relate the current and the voltage in the latter case, we use the concept of phasors. In this section, we will learn about phasor diagrams in detail. A phasor is a vector that is used to represent a sinusoidal function. It rotates about the origin with an angular speed ω. The vertical component of phasors represent the quantities that are sinusoidally varying for a given equation, such as v and i. Here, the magnitude of the phasors represents the peak value of the voltage and the current. From the figure shown above, we can see the relation between a phasor and the sinusoidal representation of the function with respect to time. The projection of the phasor on the vertical axis represents the value of the quantity. For example, in the case of a current or a vector phasor, the projection of the phasor on the vertical axis, given by vmsinωt and imsinωt respectively, gives the value of the current or the voltage at that instant. From the phasor diagram, it is easy to detect that one of two quantities are in the same phase. For example, if for a given circuit, the phasors for the voltage and the current are in the same direction for all instances, the phase angle between the voltage and the current is zero.