# 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 (H=HEAT, I=CURRENT,T=TIME,V=POTENTIAL DIFFERENCE)

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by chandraharish

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2015-09-15T00:21:45+05:30

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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

ANSWER:

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...

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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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