according to ohms law electric current is directly proportional to the potential difference across two ends then its mathematical form should be I~V why is it V~I

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Solution

If resistance is constant the current is indeed proportional to the voltage and this proportionality could be written
I = VC (or CV), where C is the conductance which is related to the resistance by CR = 1.

If we write I = VR. That equation would say that for a given voltage, current increases with resistance and that is intuitively wrong because current decreases with resistance.

So the dependence of Current from Difference of Potential and Resistance has to be written as

I = V / R

from which V = I*R

Hence V~I

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