Question

If I= Q÷T then Q=IT and V=W÷Q that is V=W÷I*T therefore v is indirectly proportional to I then how according to ohm law V=IR?​

Answer 1

Answer:

See below.

Explanation:

By Ohm's Law,

$V \propto I$

This intuitively means that a greater potential difference ( V ) will produce a higher amount of current. Now, we introduce a constant of proportionality, namely R,

$V = IR$

Where R is the resistance provided by the conductor. If does not have any relation with the formulae you mentioned as resistance is only dependent on potential difference and current.

As per you calculation,

$Q = It\\V = \frac{W}{Q}$

Then,

$V = \frac{W}{It}$

Now, by Joule's Law, the energy ( work done ) produced by a current flowing through a resistant conductor is,

$W = I^2 Rt$

Substituing the above value of W in your derived equation, gives,

$V = \frac{I^2 Rt}{It} = IR$

Actually the Joule's Law is derived from Ohm's Law. But you needed an derivation for Ohm's Law and hence I used Joule's Law.