A

Step 1: The latent heat of fusion (L) is defined as the amount of heat required to change a unit mass of a substance from solid to liquid (or vice versa) at its melting point without a change in temperature.

Step 2: When the power source is on, the power input is P watts, which means that it provides P joules of energy every second.

Step 3: When the power is turned off, the solidification occurs. The total heat energy (Q) that is released during solidification can be calculated from the time it takes to solidify (t seconds).

Q = Power x Time = P × t

Step 4: According to the definition of latent heat, the heat released during solidification is equal to the mass of the substance times the latent heat of fusion:

Q = M × L

Step 5: Setting the two expressions for Q equal to each other, we get:

M × L = P × t

Step 6: Rearranging the equation to isolate L gives us:

L = \frac{P × t}{M}

Therefore, the latent heat of fusion of the substance is \frac{P × t}{M}.