Question

An electric kettle has two heating coils. When one of the coils is connected to an a.c. source, the water in the kettle boils in $10$ minutes. When the other coil is used the water boils in $40$ minutes. If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be

• A. 8 minutes
• B. 4 minutes
• C. 25 minutes
• D. 15 minutes

Answer 1

Answer: (A)

8 minutes

Answer 2

$Q =\frac{ V ^{2}}{ R _{1}} \times t _{1}=\frac{ V ^{2}}{ R _{2}} \times t _{2}$
$=\frac{ V ^{2}}{ R } \times t$
$\frac{1}{ R }=\frac{1}{ R _{1}}+\frac{1}{ R _{2}}$
$\Rightarrow \frac{ Q }{ V ^{2} t }=\frac{ Q }{ V ^{2} t _{1}}+\frac{ Q }{ V ^{2} t _{2}}$
$\Rightarrow \frac{1}{ t }=\frac{1}{ t _{1}}+\frac{1}{ t _{2}}$
$\Rightarrow t =\frac{ t _{1} t _{2}}{ t _{1}+ t _{2}}$
$=\frac{10 \times 40}{10+40}=8$ min.