**Introduction to electric power
**James Joule (1818-1889), an English scientist, confirmed Ohm’s Law and discovered that a conductor’s ability to produce heat is directly proportional with both its resistance and the square of the current flowing through it.

**We can see that when a voltaic electricity current travels down a metallic conductor, the amount of heat that is generated in a given amount of time is inversely proportional to the conductor’s resistance multiplied by the square of the electric intensity i.e. H-PR**

Where, H=heat evolved or generated in the conductor

I = current flowing through conductor

= Resistance offered by conductor

Electric power is the rate of energy transmission into or out of a circuit that uses electricity. Energy can be supplied by a battery or released as heat by a resistor or other component of a circuit.

**Derivation:**

The potential difference applied across the conductor causes the current to flow through it. This implies that there is an electrical work done them to moving the charge in the circuit, this is called an electrical work done. Its unit is joule. Therefore,

1 joule= volt coulomb

Or , W=v*q

or , W=V x (I x t)…..( I ) (Since, I=q/t q=q x t)

Where, t is time for which the current flows.

Power is the rate of doing work and similar is the electric power that corresponds to the rate of doing electrical work done.

So, Power ( P )= work done / time

P=W/ t (ii)

Substituting equation (i) in equation (ii), we get,

P = V q /t = V (I*t)/t =VI

Power (P) = Voltage (V) x Current (I)

Hence, for any circuit element, the power is equal to the voltage difference across the element multiplied by the current.

By Ohm’s law, we have

V=IR

So the expression of power becomes

Power (P) = (IR) × I

Power (P) = I² R

Hence, electrical power is also the product of square of current flowing through a conductor and its resistance. The unit of electrical power is J/sec or watt

**Units of Electrical Power**

The unit of electrical power is J/sec or watt.

1 Watt (W) =1 Joule/second (J/S

) i.e. 1 watt is the power of an appliances which consumes energy at the rate of 1 joule per second.

Hence power is the capability of an electrical appliance, how much electrical work done due to moving the charge in the circuit in one second.

**Electrical Energy
**The power needed to do work or carry out an activity inside of an electrical circuit is provided by electrical energy.

Electrical energy is the energy that results from the kinetic or potential energy of charged particles. It is commonly known as the energy that has been transformed from electric potential energy. Electric energy is the force that results from the transfer of electrons between two points.

In other words, electrical energy means the amount of work done by an equipment during a time period of ‘t’.

Mathematically,

Energy (E )= Power (P) × Time (t)

i.e. E=P*time

It’s unit is joule or watt-second. It is very basic and small unit, for this reason wh (watt- hour) or kWh (kilo-watt-hour) is used for commercial application to measure the Consumption of electrical energy through energy metering. Generally, electric power supplier and utilities measures the electrical energy (electricity utility bill) by installing electric energy meters at the user end.

We have, E=P*t

= IV*t [.P=IV]

If 1 V voltage is applied across a circuit and 1 ampere of current is flowing through it for 1 second, then work done or amount of electrical energy would be 1 joule or watt- second

1J =1W*1s=1Ws

Different Units: 1Wh= (1*60*60)

=3600Ws

1kWh=1000Wh

=1000*60*60 Ws

=3.6 Mega Joule (MJ)