Using the formula H=I*I*R*T we get H is directly proportional to R.
but also in the second formula we have H=(V^2/R)T.. here R is inversely proportional to R. HOW IS THIS POSSIBLE??? IS R DIRECTLY OR INVERSELY PROPORTIONAL TO H



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That depends on the situation.

We have a resistor of value R, that is connected across a potential difference V.  Then a current of intensity I flows in that, where  I = V / R.   The power (instantaneous) dissipated as heat is  =  P = I² R  or   V² / R. 

Then  heat generated over time T is  H =  P T = I² R T = V² T / R


Once we understand this much, we need to know if the resistance is connected across a current source which has a fixed current  or  across a voltage source like a battery.  In this case the voltage is constant. 

In case the voltage V across R, is constant, then  H is inversely proportional to R.  In this case the current varies inversely with R and hence we have to substitute I = V/R...

 In case the current passing through R, is kept constant, then voltage across it varies directly as R varies,  then we use the formula :   H = I² R T.  Then H is directly proportional to R.

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