Q. An electric kettle boils some water in 16 min. Due to some defect, it becomes necessary to remove 10% turns of heating coil of the kettle. Now, how much time will it take to boil the same of water?
A) 17.7 min
B) 14.4 min
C) 20.9 min
D) 13.7 min
Explanation
(b) We know, $\frac{V^{2}t}{4.2\ R} = Q = ms\ d\theta$
Let,$N =$ initial number of turns
$\ R =$ resistance of the coil
$\Rightarrow R = \rho\frac{L}{A} = \frac{\rho \times N \times 2\pi r}{A}$
$\frac{V^{2}t}{4.2 \times \rho \times N \times 2\pi r} = Q = ms\ d\theta$
$\ \frac{t}{\ \ N} =$ Constant
$\therefore\frac{t_{1}}{N_{1}} = \frac{t_{2}}{N_{2}}$
$\Rightarrow \ \ = \frac{N_{2}}{N_{1}} \times t_{1} = \frac{9}{10} \times 16 =$14.4 min.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.