Question

Give the mathematical proof :

" The electric current flowing through any conductor is directly proportional to the potential different across its two ends provided its temperature remains constant "

In other sense,

" Give the mathematical proof of ohm's law ."​

Answer 1

$\huge\red{\underline {\underline {\mathfrak{Answer:-}}}}$

$\huge\green{\boxed{\bold{Ohm's\:Law}}}$

At constant temperature,the current following through a circuit is directly proportional to the potential difference across its end.

✔Current $\propto$ P.D

✔P.D $\propto$ Current

✔V $\propto$ I

✔V = RI

$\bf Where,\: R\: is\: constant \:known\:as\:Resistance.$

Limitation of Omh's Law:- Omh's law failed in the case of variable physical conditions like arranging temperature.

Answer 2

$\huge\underline\mathrm{Ohm's\:Law-}$

According to ohm's law,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀" The electric current flowing through any conductor ( metallic wire ) is directly proportional to the potential difference across its two ends provided its temperature remains the same. "

Explanation :

Let a metallic wire ( conductor ) - R

Let V, potential difference across its two ends

Let I, electric current flowing through it.

Then according to ohm's law,

Electric current $\propto$ Potential difference across its two ends

$\implies$ I $\propto$ V

$\implies$ V $\propto$ I

$\implies$ V = RI

Where, R is a constant of proportionality and is called the ohm's constant or resistance.

Now, equation can be written as :

$\huge{\boxed{\red{\rm{V\:=\:IR}}}}$

which is required mathematical form.

$\rule{200}2$

Now, what is resistance?

$\implies$ The property of any conductor to resist the flow of charge through it is called resistance.

V = IR

$\therefore$ R = $\dfrac{V}{I}$

S.I unit of resistance :

It is ohm, in the honor of scientist George simon ohm. It is represented by $\Omega$.

Ohm = $\dfrac{Volt}{Ampere}$

$\implies$ $\Omega$ = ${VA}^{ - 1}$