Question

An electric kettle rated $250V$can bring a certain amount of water to its boiling point in $8min$. If it is connected to $200V$ mains, calculate the time in which water comes to its boiling point.

Answer 1

To determine the time that water comes to its boiling point:

$\left(i\right)$Energy consumed by water in $8min$ at $250V:$

Energy$\text{E}=\frac{{\text{V}}^{2}t}{\text{R}}$

Voltage $V=250V$

Resistance $=R$

$=\frac{250\times 250\times 8\text{min}}{R}$

$\left(ii\right)$Energy consumed by water at $200~V:$

$E=\frac{V^{2}t}{R}$

$=\frac{200\times 200\times t}{R}$

By law of conversation of energy $\left(i\right)=\left(ii\right)$

$[\frac{200\times 200\times t}{R}=\frac{250\times 250\times 8}{R}]$

$t=\frac{250\times 250\times 8}{200\times 200}$

$=12.5min$

Hence, the time that water comes to its boiling point is $12.5min.$