Question

The heat produced by a $100\,watt$ heater in $2\,\min $ will be equal to
(A) $12 \times {10^3}\,J$
(B) $10 \times {10^3}\,J$
(C) $6 \times {10^3}\,J$
(D) $3 \times {10^3}\,J$

Answer 1

Hint The total amount of the heat energy produced can be determined by the power formula, by using this formula and the also by using the given information in the question, the amount of the heat energy developed can be determined.

Useful formula
The relation between the power, energy and time is given by,
$P = \dfrac{E}{t}$
Where, $P$ is the power which is given to the system, $E$ is the energy developed by the system and $t$ is the time taken to produce the energy.

Complete step by step solution
Given that,
The power given to the heater is, $P = 100\,watt$,
The time taken by the heater to produce the energy is, $t = 2\,\min $.
Now,
The relation between the power, energy and time is given by,
$P = \dfrac{E}{t}$
By rearranging the terms in the above equation, then the above equation is written as,
$E = P \times t$
By substituting the power given to the heater and the time taken by the heater in the above equation, then the above equation is written as,
\[E = 100 \times 2 \times 60\]
The multiplication of the term $60$ indicates the unit conversion of the time from minutes to hours.
By multiplying the terms in the above equation, then the above equation is written as,
\[E = 12000\,J\]
Then the above equation is also written as,
\[E = 12 \times {10^3}\,J\]
Thus, the above equation shows the energy developed by the heater.

Hence, the option (A) is the correct answer.

Note The energy developed by the heater is directly proportional to the power given to the heater and the time taken by the heater. As the power given to the heater and the time taken by the heater increases, then the energy developed also increases.