# Power triangle; definition, formula, and more to know.

Power in Alternate Current(AC) circuit consists of three elements such as active, reactive, and apparent power. These three elements are represented by a right-angle triangle known as a power triangle.

## Power triangle:

Power in Alternate Current(AC) circuit consists of three elements such as active power, reactive power, and apparent power. These three elements are represented by a right-angle triangle known as a power triangle. A power triangle is essential for the calculation of active, reactive, and apparent power if any two out of the three power is known.

### Alternative Current Power:

AC power supply is known for its power supply to a load, which periodically reverses its direction ( two directions) and changes continuously in between the minimum and maximum peak values. Then what is load? In simple language, we may say anything that consumes electric power is called load. All the consumer electrical/electronic items like computers, fans, refrigerators, bulbs, etc. are examples of loads. Ac power is mostly used for power distribution to consumers.

In an AC circuit, three basic loads are experienced which include, resistive, inductive, and capacitive.

Resistive load only consumes active power or real power. In such a circuit, power is dissipated by the resistors, where voltage and current are perfectly in phase with each other. Both the waveforms reach their peak value as well as zero value at the same time. Power flows from source to load and no power flows from load to source. In other words, we can say in resistive load, no circuit power is dissipated by loads.

Examples of resistive loads are as follows;

• incandescent light bulbs.
• toasters.
• electric heaters.

It also includes all loads that generate only heat.

Inductive load only consumes reactive power. Such a load draws reactive power from the source and feedback the power to the source again. Inductive loads take a longer time in comparison to resistive loads to develop their magnetic field. The voltage and current are out of phase with each other by 90 electrical degrees, which means both the waveforms of voltage and current reach their peak value at different points of time. Here current lags behind the voltage by 90 electrical degrees.

Examples of inductive loads are as such;

• Fans.
• Electric motors.
• Vacuum cleaners.
• Washing machines.

It further includes all the articles that have an electric motor inside.

Capacitative load Consumes reactive power like inductive load and draws reactive powers from the source and feedback the same to the source. The only difference is in a capacitative load, the current that leads the voltage by 90 electrical degrees whereas in an inductive load current lags the voltage by 90 electrical degrees. For all practical purposes, the pure capacitative load is not found, rather than having capacitance as well as resistance properties.

Examples of capacitative loads are as such;

• Capacitor banks.
• buried cables.
• Tv picture tubes.

The leading and lagging current is the cause of the reactive current in the circuit.

The above three loads consume or draw reactive or active powers as known from the above discussions. But what about the apparent power? Yes, that is there in the power triangle.

## Definition of the power triangle:

A power triangle is a right-angle triangle represented by active, reactive, and apparent power representing three sides in an AC circuit. Where the base component is an active power, the perpendicular is reactive power and the hypotenuse represents apparent power. All the above three elements are essential components to describe their relationship. Further, the power triangle is an important tool to calculate the power if any of the two power out of three power is known.

#### Active, Reactive, and Apparent power:

Now discuss the above three power elements in brief.

• The real power or often referred to as true power dissipated in the circuit is known as active power, which is actually utilized or consumed. It is also called useful or watt full power. The Active power is measured by Watt, KW, and MW. The active component draws active current and its magnitude is represented by I Cosᴓ.
• The product of the active component of current i.e; I Cosᴓ and voltage i.e; V is the active power- P and is written as VI Cosᴓ.
• A power that continuously bounces back and forth, between source and load is known as Reactive power. Reactive power helps to produce magnetic and electric fields, is stored in the circuits, and is discharged by transformers, induction motors, etc.
• The reactive elements are capacitors and inductors draw reactive power from the supply source. These circuit elements draw current in the positive half cycle and feedback the same to the supply source in the negative half cycle. Hence it is also known as useless or wattles power as it doesn’t make any useful work. Reactive power is measured by volt-ampere reactive (VAr) or kilowatt-volt-ampere reactive(kVAR) or megawatt volt-ampere reactive(MVAR). Its magnitude is represented by I Sinᴓ.
• The product of the reactive components of current i.e; I Sinᴓ and voltage i.e-V is the reactive power-Q and is written as VI Sinᴓ.
• Now apparent powerS is the combination of active and reactive power in the circuit. It is measured in VA, KVA, or MVA. It is also the product of RMS voltage and RMS current.

## The formula of the power triangle:

The formula of the power triangle defines the measurement and relationship of apparent power along with the other two power elements.

S2=P2+Q2 (S= apparent power ,P=real/active power ,Q=reactive power)

S=√p2+√Q2

S=√ VI Cosᴓ+√ VI Sinᴓ

S=VI(√Cosᴓ+Sinᴓ)

S=Vrms Irms,

Where Vrms is RMS( Root Mean Square ) voltage= Vpeak/√2 and Irms, is RMS (Root Means Square) current=Ipeak/√2.

## Conclusion:

The power triangle is an important tool to define the relationship between active, reactive, and apparent power. It is also used to calculate the power in the circuit if any two out of three power is known. Active power is often referred to as real power or watt full power, which is actually consumed. Reactive power that continuously bounces back and forth, between source and load. It is also known as useless or wattles power as it doesn’t make any useful work. Apparent power is the combination of active and reactive power in the circuit.