**electric powers**, i.e.

**active power, reactive power,**and

**apparent power**in

**alternating current (AC) circuits**.

# Electric Power

The rate of work done in an electric circuit is called **electric power**. It is represented by
the symbol *P* and is measured in
watts (*W*). The electric power is a
scalar quantity, which means it has magnitude only, and not direction.

In electrical engineering, we deal with two types of
electric circuits namely **DC circuits**
and **AC circuits**. The dc circuit is
an electric circuit followed by direct current, while the ac circuit is the
circuit followed by alternating current.

In the case of dc circuits, there is only one type of
electric power, i.e. active power. But, in the case of ac circuits, the electric
power can be of three types namely **active
power**, **reactive power,** and **apparent power**. This classification of
electric power in ac circuits is based on the nature of the circuit. Now, let
us discuss all these types of electric power one by one.

# What is Active Power?

In an alternating current (AC) circuit, the electrical power
which is actually consumed or utilized by the load is called **active power**. Active power is also
known as **true power** or **real power** or **wattful power**.

The active power is represented by the symbol *P*. It is measured in **Watts (W)**, and the larger units of
active power are **kilowatts (kW),
megawatts (MW), gigawatts (GW)**, etc. The active power is a fraction of the total
electrical power which actually runs the electric circuits or loads. Basically,
the active power is the average power in an ac circuit.

Since, in electrical circuits, the power is consumed by a resistor
only because neither a pure inductor nor a pure capacitor consumes any active
power. We know that for a resistor, the current and voltage are in phase. Thus,
the current in phase with the voltage in an ac circuit produces active or real
power. Active power is a useful component of the total electrical power in the
ac circuit.

Mathematically, the active or true power is defined as the
product of voltage (*V*) and a component
of total circuit current which is in phase with the voltage, i.e.

Active power, *P* = Voltage × Component of current in phase with the voltage

`\⟹P=V×I cosÏ•`

`\∴P=VI cosÏ•`

Here, the component *I cos **Ï•* of the total current is
called the **in-phase component** or **wattful component**. This is the
component of current that results in the active power in the circuit.

The most important thing to be noted
about active power is that it is the active power that is used for producing
light in a lamp, heat in a heater, torque in a motor, etc. The active power is
used up in the electric circuit, and therefore, it cannot be recovered. The
active power in an ac circuit can be measured using a **wattmeter**.

# What is Reactive Power?

The component of total electrical power
in an ac circuit which is neither consumed by the load nor performs any useful
work in the circuit is known as **reactive
power**. It is denoted by the symbol *Q*
and is measured in **volt-ampere reactive
(VAR)**. But, the larger units of reactive power are kVAr, MVAr, etc.

Reactive power flows back and forth in
the ac circuit which means it moves from source to load and load to source
alternatively, or we can it reacts upon itself, that is why it is called
reactive power.

As we know, in ac circuits there are
three basic circuit elements namely resistor, inductor, and capacitor. We also
know that the electric power consumed (or active power) in the inductor and
capacitor is zero. It is because the power supplied from the source to an
inductor or capacitor in one quarter-cycle is returned to the source in the
next quarter-cycle of the supply. In this way, an amount of power circulates
between the source and load, and it is called reactive power.

In the case of an inductor or a
capacitor, the current and voltage are 90° out of phase. Thus, the current in
the circuit which is 90° out of phase with the voltage results in the reactive
power flow in the circuit.

It is also important to know that
reactive power can be of two types – **lagging
reactive power** and **leading reactive
power**. A circuit element that draws a current from the source that lags
behind the voltage, then the reactive power received by the element is called
lagging reactive power. While, the circuit element that draws a current leading to the supply voltage, then draws a leading reactive power from the source. In
practice, the inductor is the element that draws lagging reactive power, and
supplies leading reactive power. Whereas, the capacitor is the element that
receives leading reactive power and supplies lagging reactive power.

Mathematically, the reactive power is
given by the product of voltage (*V*)
and the component of total circuit current which is 90° out of phase with the
voltage, i.e.

Reactive power, Q = Voltage × Component of total current 90° out of phase with the voltage

`\⟹Q=V×I sinÏ•`

`\∴Q=VI sinÏ•`

Here, the component *I sin **Ï•* of the total current
is called the **reactive component** or **wattless component, **or** quadrature power**. The reactive power
does no useful work in an ac electric circuit and only flows back and forth in
both directions in the circuit. A wattmeter does not measure the reactive power
in the circuit.

# What is Apparent Power?

The total electric power that appears to
be transferred from source to load in an ac circuit is called **apparent power**. It is denoted by the symbol
*S* and is given by the product of
applied voltage and circuit current, i.e.

`\"Apparent power",S=VI`

The apparent power is measured in **Volt-Amperes ( VA)**. The larger units of apparent power are

**kilo volt-ampere (kVA)**, M

**ega volt-ampere (MVA)**,

**Giga volt-ampere (GVA)**, etc.

The apparent power has two components
namely – active power and reactive power. Therefore, the apparent power is the
phasor sum of active power and reactive power, i.e.

Where, the magnitude of apparent power is given by,

`\S=\sqrt(P^2+Q^2 )`

# Power Triangle

A right-angled triangle that gives the
relation among apparent power, active power, and reactive power is known as a **power triangle**. The figure shows the
power triangle for a typical inductive circuit.

From the power triangle, we may note the following points-

(1). Relation among apparent, active, and reactive power:

`\S^2=P^2+Q^2`

(2). Active power:

(3). Reactive power:

(4). Power factor of the circuit:

`\cosÏ•=("Active power "(P))/("Apparent power "(S) )`

# Conclusion

Thus, in this article, we discussed different types of electric power in ac circuits. Where the active power is the useful power that does useful work in the circuit. The reactive power is the wattless power, i.e. it does not do any work in the circuit but rather flows back and forth between the source and load, and the apparent power is the total power supplied by the source into the circuit.

## 0 Comments