# Power Triangle

Updated: Jul 12, 2021

**Power Triangle** is the representation of active power, reactive power and apparent in a right angle triangle showing the relation between all three powers. Power triangle is useful in the AC circuit when current is lagging or leading with the voltage.

The current is lagging,leading or in phase with the voltage depending on the types of load. In a pure resistive load, the voltage and current are in the phase. In inductive type loads, the current lags the voltage. In capacitive loads, the current leads the voltage. The phasor diagram of voltage and current for all three types of loads is given below.

The active component of the current is ISinɸ, and the reactive component of current is I Cosɸ. When these current components are multiplied by voltage V, a power triangle is formed shown as belo**w**.

The AC circuit in which current lags or leads with the voltage draws three types of power.

Active Power

Reactive Power

Apparent Power

The power actually consumed by the load in AC circuit is called **Active Power or Real Power.** The active power is measured in watt or KW.

**Active Power( P) = VI Cosɸ**

The circuit which has reactive element like inductor and capacitor along with the resistive load draws reactive power. The reactive part of the load draws current which leads or lags the voltage, and as a result of this, the power back and forth in the reactive loads. The reactive elements consumes no active power, it draws reactive power. The reactive power is watt less power. It is measured in VAR, Kilowatt-ampere (KVAR) or MVAR.

**Reactive Power (Q) = VI Sinɸ**

Thus, the ac circuit draws active and reactive power. The reactive power increase the current in the circuit without doing any useful work.

The vector sum of the active power and reactive power is called **Apparent Power.** Apparent power(S) is measured in VA or KVA or MVA. The apparent power can be calculated by power triangle. The formula of apparent power is given below.

The following point shows the relationship between the active power, reactive power and apparent power, and the graphical representation of all these three powers is called Power Triangle.

When an active component of current is multiplied by voltage, we get active power consumed by the circuit. The active power is measured using the watt meter. The equipment takes active power to do the work. The power consumed by the motor to produce the torque, heating produced by a heater are the examples of active power.

When the reactive component of current is multiplied by voltage, we get reactive power consumed by the circuit. The equipment takes reactive power for its functioning. The motor and transformer draw reactive power as a magnetizing current for the operation. These equipment function if draws reactive power. The more reactive power is cause of poor power factor.

When the current drawn by the circuit is multiplied with circuit voltage, it gives the apparent power.

Power factor can be calculated using the power triangle.