Question

An electric heater of resistance 8 Ω draws 15 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater.

Answer 1

Step 1: Given data

The resistance of the heater coil is, $R=8\Omega$.

Current through the coil is $I=15ampere.$

Time used $t=2hours=7200seconds.$

Step 2: Joule's law of heating

1. Joule's law states that when a current I is flowing in a conductor of resistance R for a time T sec, then the produced heat on the conductor is directly proportional to the square of the electric current.
2. Joule's law is defined by the form, $H=I^{2}RT$ , where, H is the produced heat on the conductor.

Step 3: Power

1. Power is the heat energy developed in unit time. Basically, power is the rate at which heat is developed.
2. Power is defined by the form, $P=\frac{H}{t}$, where, H is the heat energy and t is the time.

Step 4: Calculation of heat energy

Now applying Joule's law,

$$\begin{gathered} H=I^{2}RT={\left(15\right)}^2\times 8\times 7200=1800\times 7200 \\ orH=1800\times 7200joule. \end{gathered}$$

Step 5: Calculation of power

As we know, $P=\frac{H}{t}$

So,

$$\begin{gathered} P=\frac{H}{t}=\frac{1800\times 7200}{7200}=1800 \\ orP=1800watt. \end{gathered}$$

Therefore, the heat developed in the heater at a rate $1800watt$.