Question

The question says
What amount of current will pass through 100 watt coil if it takes 21 seconds for the coil to just melt a lump of ice of mass 10g at 0

Answer 1

We can find the energy needed to melt the lump of ice as follows:

$$E=Pt,$$

here, $P=I^2R$ is the power dissipated by the coil, $I$ is the amount of current passed through the coil, $R=10\ \Omega$ is the resistance of the coil, $t=21\ s$ is the time needed to melt the lump of ice.

From the other hand, we can write:

$$E=mL_f,$$

here, $m=0.01\ kg$ is the mass of the ice, $L_f=3.36\cdot10^5\ \dfrac{J}{kg}.$

Finally, we can equate two expressions and find the amount of current passed through the coil:

$$I^2Rt=mL_f,$$ $$I=\sqrt{\dfrac{mL_f}{Rt}}=\sqrt{\dfrac{0.01\ kg\cdot3.36\cdot10^5\ \dfrac{J}{kg}}{10\ \Omega\cdot21\ s}}=4\ A.$$