20. Electric power

Electric power is represented by the rate at which the electrical energy is converted into some other form of energy.

 

The formula is,

 

$\begin{array}{l}\mathit{Power}=\frac{\mathit{Work}}{\mathit{Time}}\\ \\ P=\frac{W}{t}\end{array}$ ---- (eq. 1)

 

Let '\(I\)' be the current flowing through a conductor for time interval '\(t\)'. Let '\(V\)' be the potential difference across the two ends of the conductor of resistance \(R\).

 

Then, '\(W\)' is the work done to move the charge across the ends of the conductor. So, the equation is written as,

 

$W =V I t$ ---- (eq. 2)

 

Substituting the value of \(W\) in the equation of power,

 

 

Hence, the electric power is the product of the electric current and the potential difference due to which the current passes in a circuit.

 

According to Ohm's law, \(V = IR\). Now, by substituting this value in (eq. 2), we get

 

$W=I^{2}Rt$ ---- (eq. 3)

 

On substituting the above value in (eq. 1), we get

 

 

From Ohm's law, it is deduced that $I=\frac{V}{R}$. Hence, (eq. 3) becomes

 

 

Now, by substituting the above value in (eq. 1), we get

 

 

The SI unit of electric power is the watt (\(W\)). If \(1\ ampere\) of a current passes across the conductor at a potential difference of \(1\ volt\), then the electric power is given as