Understanding Phasor Diagrams in AC Circuits (Resistor, Inductor & Capacitor)

 When we deal with alternating current (AC) circuits, voltage and current continuously vary with time in a sinusoidal (sine wave) manner. Now, comparing these waves directly on a time graph becomes complicated — especially when they don’t peak at the same time.

That’s where phasor diagrams come in.

A phasor diagram is a graphical way to represent sinusoidal quantities (like voltage and current) as rotating vectors (or arrows) that show both:

• Magnitude (length of the arrow)
• Phase angle (how much one wave leads or lags another)

In simple words, phasors let us see the phase relationship between voltage and current instantly, without plotting full sine waves over time.

Let’s Understand Each Case

1. Resistor — Voltage and Current in phase

In a pure resistor, current and voltage change together.
When voltage increases, current increases too — and both reach their maximum and minimum points at the same time.

That’s why in the phasor diagram:

· Both V and I arrows point in the same direction.

· The phase angle (φ) between them is 0°.

👉 This means no phase difference — both are in phase.

2. Inductor — Voltage leads Current by 90°

An inductor resists changes in current due to its magnetic field.
When AC tries to change the current quickly, the inductor creates an induced voltage (back EMF) that opposes the change.

So, the current lags behind the voltage — it takes time for the current to rise or fall because of this opposition.

In the phasor diagram:

· The voltage phasor (V) is ahead of the current phasor (I) by 90°.

· We say:

“In an inductor, voltage leads current by 90°.”

👉 The energy is stored temporarily in the magnetic field and then released back — no net energy loss.

3. Capacitor — Current leads Voltage by 90°

A capacitor resists changes in voltage because it stores energy in an electric field between its plates.
When AC voltage changes direction, the capacitor charges and discharges continuously.

As a result:

· The current (rate of charging/discharging) leads the voltage.

· It reaches its maximum value earlier than voltage.

In the phasor diagram:

· The current phasor (I) is ahead of the voltage phasor (V) by 90°.

· We say:

“In a capacitor, current leads voltage by 90°.”

👉 The energy is stored in the electric field and given back in each AC cycle.

Understanding Phase Angle (φ)

The phase angle represents how much one waveform is ahead or behind another in time.

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Conclusion

Phasor diagrams provide a simple and powerful way to understand the phase relationship between voltage and current in AC circuits. Instead of analyzing complex sinusoidal waveforms over time, phasors allow us to visually compare magnitude and phase angle using rotating vectors.

In a pure resistor, voltage and current remain in phase. In an inductor, voltage leads current by 90°, while in a capacitor, current leads voltage by 90°. These phase relationships are fundamental in understanding the behavior of AC circuits and form the basis for analyzing more complex electrical and electronic systems.

By using phasor diagrams, engineers and students can easily study AC circuit behavior, power relationships, impedance, and signal interactions in a much clearer and more intuitive way.