Question

State and explain Joule's Law of Heating?

Answer 1

Step 1. Statement of Joule's law

Joule’s law of heating states that, when a current $\text{'}i\text{'}$' passes through a conductor of resistance $‘R’$for time$‘t’$then the heat developed in the conductor is equal to the product of the square of the current, the resistance and time.

Step 2. Mathematical explanation

Let $H$ be the heat produced when a current $\text{'}i\text{'}$passes through a conductor of resistance $‘r’$for time$‘t’$ then

1. $H\propto i^2$
2. $H\propto R$
3. $H\propto t$

$$\begin{gathered} \therefore H\propto i^{2}Rt \\ \Rightarrow H=\frac{1}{J}{i}^{2}Rt \end{gathered}$$

Where $J=4.2\mathrm{joules}/\mathrm{cal}$

We know that $V=iR$ where $V$ is is the voltage, $i$ is the current and $R$ is the resistance then

$$\begin{gathered} H=\frac{1}{J}{i}^{2}Rt \\ =\frac{1}{J}{\left(\frac{V}{R}\right)}^{2}Rt \\ =0.24·\frac{1}{R}·V^2·t\left[\because \frac{1}{J}=\frac{1}{4.2}=0.24\right] \end{gathered}$$