Question

From the formula I2RT heat is directly proportional to Resistance ... And from the formula V2T/R heat is now inversely proportional to Resistance.

Why so? ​

Answer 1

In equation H = I²Rt. If I is constant, only then you can say that H is directly proportional to R.

Illustration : Household electricity supply has a rating of 220V (in India), but current is not rated constant, i.e. the voltage (V) is constant but Current (I) is variable.

Therefore in Equation H = I²Rt, if we increase R, I will decrease (since I = V/R). Thus in this case based on this equation we cannot comment on the proportinality of H and R.

That is why we substitute the value of I = V/Rin equation H = I²Rt and obtain another equation H = V²t/R.

In this new equation V²t is a constant (V = 220 V).

Thus we can say H = k/R.

Or H is inversely proportional to R.

On the other hand if we have a constant current supply (certain batteries have a constant current rating), then equation H = I²Rt would make more sense in computing dependancy of H on R, and we will be able to say that H is directly proportional to R.

I hope you like my answer.