Question

An electric iron is rated 220V, 2kW. If the iron is used for 2h daily, find the cost of running it for one week if it costs Rs. 4.25 per kWh.

Answer 1

Hint: Power is defined as the rate of energy consumed or dissipated by a device with time. i.e. $P=\dfrac{E}{t}$. Use this formula and find the total energy consumed for a week in the units of kWh. Then multiply that value by 4.25 to find the total cost.

Formula used:
E=Pt

Complete step by step answer:
The electric iron is rated 220V, 2kW. This means that if a potential difference of 220V is applied across the iron then it will produce a power of 2kW.
An electric iron acts as a resistor that has some resistance. When a current passes through a resistance, the resistance consumes some amount of energy and this energy is dissipated as heat energy. This is the principle on which an electric iron works.
The power of heat produced in a resistance with a constant potential difference is given as $P=\dfrac{{{V}^{2}}}{R}$.
It is given that the cost of energy consumption is Rs. 4.25 per kWh. Hence, let us first find the total energy consumed by the iron in one week.
The power of the iron is 2kW. Power is defined as the energy consumed in one unit of time. Therefore, this means that the iron consumes an energy of 2kJ in one second.
Hence, for 2 hours it will consume an energy equal to $E=2\times {{10}^{3}}W\times 2hr=2\times {{10}^{3}}W\times 2\times 3600\operatorname{s}=144\times {{10}^{5}}J$.
1 kWh is equal to $3.6\times {{10}^{6}}J$.
$\Rightarrow 1J=\dfrac{1}{3.6\times {{10}^{6}}}kWh$
Therefore,
$E=144\times {{10}^{5}}\times \dfrac{1}{3.6\times {{10}^{6}}}kWh$
$E=4kWh$
Therefore, for one day the iron consumes an energy of 4kWh.
For a week, the iron will consume a total energy of $4\times 7kWh=28kWh$.
For 1kWh, the cost is Rs 4.25.
Therefore, the cost for energy consumption of 28kWh will be $28\times 4.25=119$ rupees.

Note: The formula for energy E=Pt is applicable only when the power is constant or when there is a uniform rate of consumption or dissipation of energy.
If the power is not constant the energy $E=\int{Pdt}$.