An electric kettle has two coils. When one coil is switched on, it takes 15 minutes to boil the water, and when the second coil is switched on, it takes 30 minutes. How long will it take to boil the water if both coils are used in series and in parallel, respectively?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 45 min, 10 min
A coil of resistance \( R \) on the supply voltage \( V \) produces Joule heat \( H=V^{2}t/R \) in time \( t \). The same heat is needed to boil the water every time and \( V \) is fixed, so the time is proportional to the resistance, \( t\propto R \). The times therefore combine in the same way as the resistances.
In series the resistances add, \( R_s=R_1+R_2 \), so the times add:
\( \begin{aligned} t_s &= t_1+t_2 \\ &= 15\,\mathrm{min}+30\,\mathrm{min} \\ &= 45\,\mathrm{min} \end{aligned} \)
In parallel \( 1/R_p=1/R_1+1/R_2 \), so for the time:
\( \begin{aligned} \frac{1}{t_p} &= \frac{1}{t_1}+\frac{1}{t_2} \\ &= \frac{1}{15\,\mathrm{min}}+\frac{1}{30\,\mathrm{min}} \\ &= \frac{3}{30\,\mathrm{min}} \\ &= \frac{1}{10\,\mathrm{min}} \end{aligned} \)
\( t_p=10\,\mathrm{min} \)