Question

derive mathematical form of ohms law
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IT IS OF CLASS X

Answer 1

Statement:– Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of the conductor,provided physical conditions of the conductors such as temperature,mechanical strain etc. Are kept constant i.e. IαV

Or VαI or V= RI

Or V/I=R=a constant

Where R is known as resistance of the conductor . It depends upon the length ,shape and the nature of the material of the conductor. The variation between potential difference (V) and current (I) through a conductor is a straight line.

Deduction of Ohm’s Law:

As drift velocity is given by V

d=eEt/m

But Electric field across the conductor of length l is

E=V/l

Thus V

d=e V/ml

Also, I=Anev

By putting value of v

in the equation of I (equation 1 of ),we get

I=Ane(eV/ml)=(Ane^22/ml)V

Or V/I=ml/Ane^2=R

Where R is a constant for a given conductor. It is known as the resistance of the conductor.

Thus V=RI

This is Ohm’s law.

Answer 2

Explanation:

Step-by-step explanation:

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf \pink{OHM'S \: LAW}$

At the constant temperature and pressure the current flowing in any circuit is directly propotional to the potential difference.

→ potential difference is directly proportional to the current.

hence

v = I × R

Here

v is voltage

I is current

and

R is constant called resistance.

Now ,

Proof :-

Let any conductor having length l.

$\bf{E \: = \frac{v}{l} ......(1)}......(1)$

I = neAVd

$\bf \implies \: neA \frac{eE}{m}$

$\bf \implies \: i \: = \frac{ {ne}^{2} AE}{m}$

$\bf \implies \frac{ {ne}^{2} Av}{lm}$

$\bf \implies \: \frac{ {ne}^{2} A \times t}{lm}$

$\bf \implies \frac{v}{i} = \frac{ml}{ne ^{2} A \times t}$

$\bf \implies \frac{v}{i}= constant$

$\bf\huge{v = iR}$