Question

An electric kettle rated at $220V$, $2.2KW$ works for 3 hours. Find the energy consumed and current drawn.

Answer 1

Hint: Electric kettle is an appliance based on thermal effects of current. It is the heating effects of current when it flows through a conductor. More is the time consumed, more will be the energy consumed and amount of drawn current from the source. We will first calculate the energy consumed and then the current drawn.

Complete step by step answer:
Let’s first calculate the energy the kettle consumes.
Energy of an electrical appliance is the power consumed in unit time.
Mathematically, $E = Pt$
Where $E$ is the energy consumed
$P$ is the power of the appliance
$t$ is the time expended
Given in the question is that, the power of the electric kettle is $2.2KW$ and the time it has been used is 3 hours.
So, after substituting these values, energy consumed by the kettle is,
$E = 2.2 \times 3$
$ \Rightarrow E = 6.6KWh$
So, the energy consumed is $6.6KWh$ or $6.6units$. This answers our first part of the question.
Now, let’s define power.
Power of an electrical appliance is the rate at which electric current does work against the resistance of a conductor.
Mathematically, it is given by,
$P = \dfrac{W}{t}$
Where $P$ is the power of the appliance
$W$ is the work done by the current in time $t$ .
Work done by the conductor as per Joule’s law of heating is given by,
$W = VIt$
Where current $I$ does $W$ amount of work against a potential difference of $V$ across the conductor in time $t$ .
Putting this value in the expression of electric power, we get,
$ \Rightarrow P = \dfrac{{VIt}}{t}$
$ \Rightarrow P = VI$
Thus power of a conductor or appliance is the product of potential difference and amount of current flowing through it.
We are given the data that the potential difference is $220V$ and power is $2.2KW$ or $2200W$
Substituting these values we get,
$ \Rightarrow 2200 = 220 \times I$
$ \Rightarrow I = 10A$

Thus the amount of current drawn from the source will be $10A$ .

Note:The other expression for Joule’s law of heating for a conductor is $W = {I^2}Rt$, because in Ohm’s law, $V = IR$. The key points are, electrical energy is power consumed in unit time and electrical power is the product of potential difference and amount of current. Also be careful in calculations in terms of the system of units used.