# Power Vs Energy-Difference between Power and Energy

This page on Power vs Energy describes **difference between power and energy**.
It mentions types of power e.g. average power, pulse power, modulated power and RMS power.
Units of power and energy as well as formula are also mentioned.

These two are two different terms used to represent same thing in different units of measure.
Power is energy per unit time.
Power is proportional to energy change rate of one joule per second i.e. 1 W = 1 J/Second .

For example, An electric lamp having power of 100 W changes 100 J of electrical energy into heat and light energy each second.

## Power

The figure-1 depicts the circuit consists of resistor in series which is fed by AC source.
Power of a CW signal at frequency of f0 (=1/T0) is expressed as follows:

Where, T0 = AC period of signal

Vpeak = Peak Voltage

Tpeak = Peak Current

φ = phase angle between voltage and current waveform

n = Number of Ac periods

The unit of power is watt or milliwatt or microwatt. The power used for radio frequency(RF) can
be expressed in dBm, dBW, dBµW etc.

Power is measured using power meter.
Refer Power meter measurement basics for more information.

This provides the equation as mentioned below.

This equation can be obtained for n = (1,2,3,....)

## Energy

RF energy is measured for EM wave which consists of electric (E) and magnetic field (H) components.
E field strenth is measured in V/m and H field strength is measured in A/m.
RF energy is referred as power density or power per unit area.
RF energy is measured in units of W/m^{2}.
Energy is measured using energy meter or smart meter.

Energy of the DC voltage across a resistor is expressed as above. The equations when V is DC voltage as well as when C is sinusoidal voltage is also mentioned.

## Types of Power-Average Power, Pulse power, Modulated Power, RMS Power

**Average Power**:

For average power, energy transfer rate is averaged over some time period.
For Continuous Wave signal lowest and highest frequency are same and hence both average power and power are equal.
This is very useful for amplitude modulated waveform. In this case, power is averaged over many periods of
the modulated signal. Average power is expressed as follows.

In the equation Tl is the period of low frequency component of I(t) and V(t).

**Pulse Power**:

The power which is averaged over pulse width of size τ is known as pulse power.
It is expressed as follows:

**Modulated Power**:

In the case of modulated or pulsed power measurement, shape of the signal is very important.
For signal having higher peak to average ratio, crest factor is used. This crest factor is used for both voltage or power.

ζ = peak value/rms value

The crest factor for sinusoidal wave (pure) is ζ_{sine} = 1.41

For Pulsed signal it is equal to ζ_{pulse} = (1/duty cycle)^{0.5}

When crest factor increases, energy content of signal having high order of harmonics will also increase.

**RMS Power**:

It is referred as root mean squared power. energy equations for dc voltage across a resistor have been mentioned above.
For rms power, effective voltage is to be determined as per equation mentioned below.

By substituting effective voltage into power equation, rms power can be expressed as follows:

P = (V_{eff})^{2}/R

The RF, electrical and electronics engineers can utilize this basic knowledge on power, energy and types of power for test and measurement and other application areas.

Following table summarizes important differences between power and energy.

Feature |
Power |
Energy |
---|---|---|

Definition | Power equals multiplication of voltage and current in the circuit. It is also proportional to energy change rate in one second. | RF energy is equal to power density or power per unit area. |

Unit of measurement | Watt, dBW, dBm, dBµW | Joule or W/m^{2} |

measuring equipment | Power meter | Energy meter, smart meter |

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