Question

An electric heater has a rating of $2kW$, $220V$. The cost of running the heater for $10$ hours at the rate of Rs. $350$ per unit is Rs.
A. $216$
B. $165$
C. $209$
D. $7000$

Answer 1

The rating mentioned on any electric appliance is given in the units of $kWh$(kilowatt-hour) and $V$(volts). They specify the power given by the appliance during its run-time and the voltage required for the appliance to work respectively. We can calculate the energy consumed by the device while it is working and consecutively the cost of energy expenditure can also be calculated.

Complete step-by-step solution:
Power is the work done per unit time by an object. It is also the energy consumed or delivered per unit time.
$\begin{aligned} & Power=\dfrac{W}{t} \\\ & \Rightarrow Power=\dfrac{E}{t} \\\ \end{aligned}$
Where,
$E=$ energy consumed
$W=$ work done
$t=$ time taken

According to the power rating given, we know that our device consumes 2 kilowatts of energy (or 2 kilo Joules of electric energy per second).
The total energy consumed in $10$hours is given as:
Energy= power $\times$ time
$\begin{aligned} & \Rightarrow E=\left( 2kW \right)\left( 10h \right) \\\ & \Rightarrow E=20kWh \\\ \end{aligned}$
Hence, the total energy consumed is $20kWh$.

Now, we know that one commercial unit of electric energy is one-kilowatt hour,$1kWh$.
Since the cost of one unit of electricity or one-kilowatt hour of electric energy is Rs. 350,
therefore, the cost of $20kWh$ or 20 units of electricity is calculated as:
Cost = $\left( Rs.350 \right)\left( 20units \right)$
$\Rightarrow$ Cost = $Rs.7000$

Therefore, the correct option is (D) $Rs.7000$.

Note:
Electric appliances consume electric energy and convert it into heat energy and light energy respectively. This electric energy is delivered to our households by large generators as the generators convert their rotational kinetic energy into electric energy. Hence, in daily life, we do not pay for the voltage or current, but we pay for the energy consumed by us during our day-to-day activities.