$100 \mathrm{J}$ of heat is produced each second in a $4\mathit{ \Omega }$ resistance. Which of the following is the potential difference across the resistor?

$100 \mathrm{J}$ of heat is produced each second in a $4\mathit{ \Omega }$ resistance. The potential difference across the resistor is $20 \mathrm{V}$.
Given,                                                                                                                                            

Resistance, $\mathrm{R}=\mathrm{ }4\mathrm{ \Omega }$, Time$, \mathrm{t}=\mathrm{ }1 \mathrm{s}$
heat produced, $\mathrm{H}=\mathrm{ }100 \mathrm{J}$We know that,                                                                                                                             

$\Rightarrow \mathrm{H}=\frac{{\mathrm{V}}^2}{\mathrm{R}}\mathrm{t}$                                                                                                                                   

Therefore, the potential difference across the resistor, 

$\mathrm{V}=\sqrt{\frac{\mathrm{HR}}{\mathrm{t}}}$                                                                       

$\Rightarrow \mathit{V }=\sqrt{\frac{100\times 4}{1}}$
$= 20\mathit{ V}$