Question

A source of potential difference $V\,volt$ sends current of $I\,A$ in a circuit for time $t\,\sec$. Write expression for (a) electrical energy supplied by the source, and (b) electrical power spent by the source.

Answer 1

Hint In general, the work done is equal to the electrical energy, so by using the work done formula the electrical energy is determined. And by using the electrical power formula, then the electrical power can also be determined by using the work done.

Useful formula
The work done in the moving charge is given by,
$W = QV$
Where, $W$ is the work done by the source, $Q$ is the charge of the source and $V$ is the potential energy of the source.
The electrical power in the circuit is given by,
$P = \dfrac{W}{t}$
Where, $P$ is the electrical power in the circuit, $W$ is the work done by the source and $t$ is the time taken.

Complete step by step answer
Given that,
The source will have the potential difference of, $V\,volts$,
The source will send the current of, $I\,A$,
The time taken by the source is, $t\,\sec$.
(a) Electrical energy supplied by the source:
Now,
The work done in the moving charge is given by,
$W = QV\,................\left( 1 \right)$
The charge of the circuit is given by,
$Q = It$
By substituting the above equation in the equation (1), then the equation (1) is written as,
$W = VIt$
Therefore, the work done is equal to the electrical energy, then the above equation is written as,
$E = VIt$.
Thus, the above equation shows the electrical energy.
(b) Electrical power spent by the source:
Now,
The electrical power in the circuit is given by,
$P = \dfrac{W}{t}\,........................\left( 2 \right)$
By substituting the work done equation in the equation (2), then the equation (2) is written as,
$P = \dfrac{{VIt}}{t}$
By cancelling the same terms in the above equation, then the above equation is written as,
$P = VI$

Thus, the above equation shows the electrical power.

Note The electrical energy is directly proportional to the potential difference, current and the time. As the potential difference, current and the time increases, then the electrical energy also increases. The electrical power is directly proportional to the potential difference and current increases, then the electrical power also increases.