Question

A current of $10A$flows through an electric oven of resistance $80\Omega$ for $1hour$. Calculate the rate of generation of heat.

Answer 1

Step 1: Given data and formula used

Given data:

1. Current flowing through an electric oven is $I=10A$
2. Resistance of the oven is $R=80\Omega$
3. Time for which current flows is $t=1hour=1\times 3600s=3600s$

Formula:

Firstly, we have to find the amount of heat produced by an electric oven.

According to Joule's law of heating, the amount of heat produced $\left(H\right)$ by an electric oven is

$H=I^{2}Rt$

Step 2: Finding the amount of heat produced

Substituting the values of current, resistance, and time into the formula to calculate the heat.

$$\begin{gathered} H={\left(10A\right)}^2\left(80\Omega \right)\left(3600s\right) \\ H=100\times 80\times 3600 \\ H=28800000J \end{gathered}$$

Step 3: Finding the rate of generation of heat

The rate of generation of heat $\left(R\text{'}\right)$ is given by

$R\text{'}=\frac{H}{t}$

Substituting the values of heat produced and time into the formula to calculate a rate.

$$\begin{gathered} R\text{'}=\frac{28800000J}{3600s} \\ R\text{'}=8000J/s \end{gathered}$$

Thus, the rate of generation of heat is $8000J/s$.