An induction heater employs a coil of turns carrying an alternating current at

PHYSICS · Single correct · CBSE · Physics · Electromagnetic Induction · Electromagnetic Induction

Problem

An induction heater employs a coil of

20

turns carrying an alternating current at

10\,\text{kHz}

. The magnetic flux linked with the aluminium work-piece is given by

\Phi(t)=2\times10^{-5}\sin(2\pi f t)\,\text{Wb}

per turn. The work-piece has electrical resistance

0.50\,\Omega

, mass

0.50\,\text{kg}

and specific heat capacity

900\,\text{J kg}^{-1}\,^{\circ}\text{C}^{-1}

. Assuming all induced electrical power is converted to heat, the approximate time needed to raise its temperature by

20\,^{\circ}\text{C}

is (a)

7.1\,\text{s}

(b)

3.6\,\text{s}

(c)

14.2\,\text{s}

(d)

28.4\,\text{s}