Question

A student boils the water in an electric kettle for 20 minutes. Using the same main supply, he wants to reduce the boiling time of water. To do so, should he increase or decrease the length of the heating element? Justify your answer

Answer 1

The length of a conductor is directly proportional to its resistance,

$P=\frac{V^2}{R}$

$tosupplymorepowertotheheatingelement,weneedtoreducetheR,$

$thereforereducethelength.$

At solution:

$H=I^{2}Rt$

$\because V=IR$

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

$\because heatingamountissame,\therefore H_1=H_2$

$itisgiventhatsupplyissame,$$\therefore V_1=V_2$

$\frac{V^2}{R_1}{t}_1=\frac{V^2}{R_2}{t}_2$

$\frac{t_1}{t_2}=\frac{R_1}{R_2}$

$\because t_2<t_1$

$\therefore R_2<R_1,\therefore l_2<l_1$

Hence, to reduce the heating time on the same supply, we must reduce the length.