Question

An electric heater of power 3kW is used for 10h. How much energy does it consume? Express your answer in joule.
A. $1.08\times {{10}^{5}}$
B. $1.08\times {{10}^{8}}$
C. $1.08\times {{10}^{7}}$
D. $1.08\times {{10}^{3}}$

Answer 1

As a first step, give a brief definition of the power of an electric heater. From the very definition you will understand its relation with the energy consumed. As all the values that are needed to be substituted are given in the question, you could easily find the answer. Also, convert the value thus obtained into Joules.

Formula used:
Power,
$P=\dfrac{W}{t}$

Complete Step by step solution:
In the question we are given an electric heater whose power is known to be 3 kilo-watts when it is used for 10 hour duration. Using these values, we are supposed to find the energy consumed by this electric heater in joules.

In order to answer this we have to understand what exactly the power of an electric heater is. The power of a heater can be defined as the amount of energy transferred or converted per unit time. This can be expressed mathematically as,
$P=\dfrac{W}{t}$
So the work done would be,
$W=Pt$

Substituting the values,
$W=3\times 10=30kWh$

Now, let us convert the work done or the energy consumed in kWh to joules. This can be done by multiplying the value with$3.6\times {{10}^{6}}$.

Therefore, the energy consumed by the given electric heater will be,
$W=30\times 3.6\times {{10}^{6}}J$
$\therefore W=1.08\times {{10}^{8}}J$

Hence, we have found the required value to be$1.08\times {{10}^{8}}J$. Option B is correct.

Note:
The basic working principle of an electric heater is known to be Joule heating. It consists of a resistor wire, normally a metal-alloy like the nichrome wires that convert the electrical energy into heat energy. The efficiency of these devices is known to be 100% and it can be also made further effective by certain adjustments.