A current of 5.0 A  flows through a 12$\mathrm{\Omega }$ resistor. What is the rate at which heat energy is produced in the resistor?

Given, 

Current, I = 5A
Resistance, R =$12 \mathrm{\Omega }$. 

We know from Joule’s heating law :
Heat energy, $\mathrm{H}={\mathrm{I}}^2\mathrm{Rt}$ .....(1)
The rate at which heat energy is produced in the resistor is power.

We know, 

Power = H/t
From 1 we get, $\mathrm{H}/\mathrm{t}=\mathrm{ }{\mathrm{I}}^2\mathrm{R}$
$\Rightarrow \mathrm{H}/\mathrm{t}=\mathrm{ }{5}^2\times 12$ 

$\Rightarrow \mathrm{H}/\mathrm{t}=25\times 12$
$\Rightarrow \mathrm{H}/\mathrm{t}=\mathrm{ }300 \mathrm{joule}/\mathrm{s}$ or Watt.
 When a current of 5.0A flows through a $12\mathit{ \Omega }$ resistor, the rate at which heat energy is produced in the resistor is 300W.