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Electric Power - (Concept)

 Electric Power-

When an electric current flows through a conductor, electrical energy is used up and we say that the current is doing electrical work. So electric power is the electrical work done per unit time.

Or 

The rate at which electrical work is done or the rate at which electrical energy is consumed is called electric power.

That is Power $=\frac{\text { Work done }}{\text { Time taken }}$ or $\quad P=\frac{W}{t}$
Unit of Power-
The SI unit of electric power is watt which is denoted by the letter W. The power of 1 watt is a rate of working of 1 joule per second.

$$
\text { That is } 1 \text { watt }=\frac{1 \text { joule }}{1 \text { second }}
$$


Formula for Electric Power-
Consider a current I flowing through a resistor of resistance R. Let the potential difference across it be V . Let t be the time during which a charge Q flows across.

The work done in moving the charge Q through a potential difference V is VQ.
Therefore, the source must supply energy equal to $V Q$ in time $t$.
Hence the power input to the circuit by the source is

$$
P=V \frac{Q}{t}=V I
$$
 

I.e  Electric power = Potential difference × Current

For unit of power 

We get 1 watt = 1 volt × 1 ampere

So we can define that one watt is the power consumed by an electrical device which when operated at a potential difference (or voltage) of 1 volt carries a current of 1 ampere.

Some Other Formulae for Calculating Electric Power-

  • Power P in terms of I and R

Power, $\quad P=I^2 \times R$ where $I=$ Current and $\quad R=$ Resistance
- Power $P$ in terms of $V$ and $R$

Power, $\quad P=\frac{V^2}{R}$ where $V=$ Potential difference or Voltage and $\quad R=$ Resistance

 

 Electrical Energy-

 The electrical energy consumed by an electrical appliance is given by the product of its power rating and the time for which it is used.

That is Electrical energy = Power × Time or E = P × t

 The commercial unit of electric energy is a kilowatt-hour (kW h), commonly known as a ‘unit’.

And     1 kW h = 3.6 × 106 joule (J)

The heat produced in a wire-

Assuming that all the electrical work done or all the electrical energy consumed is converted into heat energy.

Then 

Heat produced, $H=P \times t=I^2 \times R \times t$
This formula gives us the heat produced in joules when a current of I amperes flows in a wire of resistance R ohms for time t seconds. This is known as Joule's law of heating.

Joule's law of heating-
According to Joule's law of heating, the heat produced in a wire is directly proportional to
(i) square of the current $\left(1^2\right)$
(ii) the resistance of the wire (R)
(iii) time ( t ), for which current is passed

And It is given by the formula $H=I^2 \times R \times t$

 

Exam Chapter
JEE FOUNDATION Electricity
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