Question

In an electric kettle, water boils in 10 minutes after the kettle is switched on. With the same supply voltage if the water is to be boiled in 8 minutes, should the length of the heating elemnet be increased or decreased ? Explain .

Answer 1

For a given supply voltage, heat produced in time t is
`H = V^(2)/R t = V^(2)/(rho l//A) t = (V^(2)At)/(rho l)` i.e., `H prop (t)/(1)`
`:. H_(1)/H_(2) = t_(1)/t_(2) xx l_(2)/l_(1)` As `H_(1) = H_(2)`, so `1 = t_(1)/t_(2) xx l_(2)/l_(1)`
or `l_(2)/l_(1) = t_(2)/t_(1) = 8/10 lt 1 or l_(2) lt l_(1)`
It means the length of the heating wire should be decreased.