Question

A heater boils 1 kg of water in time $t_1$ and another heater boils the same water in time $t_2$. If both are connected in series, the combination will boil the same water in time:

• A. $\frac{t_1{t}_2}{t_1+t_2}$
• B. $\frac{t_1{t}_2}{t_1-t_2}$
• C. $t_1+t_2$
• D. $2(t_1+t_2)$

Answer 1

Answer: (C)

$t_1+t_2$

We know
$P=\frac{Q}{t}$ .......(1)
Here, both heaters are connected in series and the combination will boils same water in time $t_1$ and $t_2$ with powers $P_1=\frac{Q}{t_1}$ and $P_2=\frac{Q}{t_2}$
Hence,
$\frac{1}{P^{\prime }}=\frac{1}{P_1}+\frac{1}{P_2}$
$\frac{1}{P^{\prime }}=\frac{1}{\frac{Q}{t_1}}+\frac{1}{\frac{Q}{t_2}}$
$\frac{1}{P^{\prime }}=\frac{t_2}{Q}+\frac{t_2}{Q}$
$\Rightarrow P^{{}^{\prime }}=\frac{Q}{t_1+t_2}$
Comparing with (1), we get,
$t=t_1+t_2$