Question

A heating coil takes 6 min to boil certain amount of milk. Another heating coil takes 3 min to boil same amount of milk. Supply voltage is same. When the coils are connected in parallel, time taken to boil same amount of milk is

• A. 9 min.
• B. 2 min.
• C. 4.5 min.
• D. 3 min.

Answer 1

The Correct Option is B

For heating coil 1,
$H= \frac{V^{2}}{R_{1} }t_{1} or R_{1 } = \frac{V^{2}}{H} t_{1} $
For heating coil 2,
$H =\frac{V^{2}}{R_{2}} t_{2} or R_{2} = \frac{V^{2}}{H}t_{2} $
Now, for parallel combination of coils,
$H= \frac{V^{2}}{R}t$
where, $ R = \frac{R_{1} \times R_{2}}{R_{1} + R_{2} } = \frac{V^{2} \left(t_{1} \times t_{2}\right)}{H\left(t_{1} + t_{2}\right)} $
or, $ H = \frac{V^{2}}{\frac{V^{2} \left(t_{1} \times t_{2}\right)}{H\left(t_{1} +t_{2}\right)}}\times t$
or,$ t = \frac{t_{1}\times t_{2}}{t_{1}+t_{2}} = \frac{6\times 3}{6+3} = 2 min$