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) $2160$
B) $7000$
C) $2000$
D) $3500$

Answer 1

Hint: The question is based on energy calculations specifically relation between powers consumed and energy generated, the relationship between units of energy consumed and the cost of it.

Formula used:
(I) ${{E = }}\;{{P}} \times t$
Where, $E$is total energy, $P$is power and $t$is time
So, $P = \dfrac{E}{t}$
(ii) ${{1}}\;{{Unit}}\,{{ = }}\;{{1000W}}$ In $1$ hour.
${{1KWh = }}$$ = $ Energy consumed at the rate of ${{1000}}\;W$ per hour.

Complete step by step solution:
Given, here an elective heater has a rating of \[{{2kW}}\] which means it will consume ${{2000J}}$ of energy in one second time.
We know that,
Power is energy consumed per unit time.
So, ${{P}}\;{{ = }}\;{{2kW}}$
$ \Rightarrow {{P = }}\;{{2000W}}$
This power is generated in one second & we have to calculate (for$10$hours) energy consumed:
So, $t = 10h$
$ \Rightarrow t = \;36000\operatorname{s} $
We know that
Total energy
 $E = P \times t$
Putting the values we get,
$ \Rightarrow {{E = }}\;{{2KW \times 10hr}}$
$ \Rightarrow E = 2000W \times 10 \times 3600\sec $
$ \Rightarrow E = 72 \times {10^6}J$
We know that one unit ${{ = 1000W}}$ per hour
The cost of running the heater is given as Rs $350$ per unit, so we will convert energy in Joules to $kWh$.
$
  {{E}}\;{{ = 72 \times 1}}{{{0}}^{{6}}}{{J}} \\
  {{1KWh}}\;{{ = }}\;{{3}}{{.6 \times 1}}{{{0}}^{{6}}}{{J}} \\
 $
So energy in ${{kWh}}$
$\therefore E{{ = }}\;\dfrac{{{{72 \times 1}}{{{0}}^{{6}}}}}{{{{3}}{{.6 \times 1}}{{{0}}^{{6}}}}}{{ = }}\;{{20}}\;{{KWh}}\;{{ = }}\;{{20}}\;{{Unit}}$
So, calculating the cost of running the heater for one unit the cost is Rs $350$
$\therefore $ For $20$ units the cost ${{ = }}\;{{RS}}\;{{350 \times 20}}\;{{ = }}\;{{Rs}}\;{{7000}}$

Hence, Option (B) is correct.

Note:
Alternate solution: The heater is consuming ${{2kW}}$ of power so in $1$ hour it will consume ${{2kW}}$ of energy which is two units of energy. So in $10$ hours it will consume $20$ units of energy. As one unit cost is ${{Rs}}\;{{350}}$ is $20$ units will cost Rs \[7000\left( {20 \times 350} \right)\].
${{1KWh}}$ is defined as ${{3}}{{.6 \times 1}}{{{0}}^{{6}}}J$ amount of energy and that is considered as one unit in electricity bills.