Question

An electric fan runs from the $220V$ mains. The current flowing through it is $0.5A$. At what rate is the electrical energy transformed by the fan? How much energy is transformed in $2\text{ min}$?

Answer 1

Hint: This problem can be solved by using the direct formula for the consumption of power by an electrical device in terms of the current across it and voltage across it. The rate of transformation of energy will be nothing but the power.
Formula used:
$P=VI$
$E=P\times t$

Complete answer:
We will find out the rate of transformation of energy (or the power consumed) in terms of the current through the fan and the voltage across it.
The power $P$ consumed by an electrical device when the current through it is $I$ and the voltage across it is $V$ is given by
$P=VI$ --(1)
Also, the energy $E$ consumed in time $t$ by a device running at power $P$ is given by
$E=P\times t$ --(2)
Now let us analyze the question.
Since, the fan runs on $220V$, the voltage across it is $V=220V$.
The current through the fan is $I=0.5A$.
Let the power consumed by the fan be $P$. This is the same as the rate at which energy is transformed by the fan.
Let the energy transformed in $t=2\text{min}$ be $E$.
$t=2\min =2\times 60\operatorname{s}=120\operatorname{s}$ $\left( 1\min =60s \right)$
Now, using (1), we get
$P=220\times 0.5=110W$ --(3)
Also, using (2), we get
$E=P\times 120$
Putting (3) in the above equation we get
$E=110\times 120=13200J$
Hence, the rate of transformation of energy by the fan is $110W$ while the amount of energy transformed in $2\min $ is $13200J$.

Note:
Students must note that the direct formula $P=VI$ can be applied for AC only for the root mean square (rms) voltage value. This is because the voltage and the current do not remain constant for an AC input cycle. However, in the question, the value of voltage given to us is the rms voltage. If in the question, it is not mentioned that the voltage input is of what kind, then students must assume that the input given is the rms value of the voltage cycle.