Question

prove ohm's law mathematically

Answer 1

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

$\bf \pink{ohms \: law}$

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.

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



I = neAVd



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



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


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


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



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


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



$\huge{v = iR}$

$\huge \green{\boxed{ \boxed{PROVED}}}$

Answer 2

Heya,

__________^_^___________

Ohm's Law states that all physical condition (temperature, density, length, area of cross - section, etc.) of a conductor remaining same, the current flowing through it is directly propotional to the potential difference at its ends.

___________☆☆☆_____________

Ohm's Law Mathematically,

A resistor AB of unknown value is connected in series of a cell, through a key, an ammeter and a rheostat as shown in the fig. A voltmeter is attached in parallel to resistor AB.

On closing the circuit with a key, the ammeter and voltmeter show the current flowing through the circuit and the potential difference at the ends of the resistor AB respectively.

The current in the circuit can be changed by adjusting the slider of the rheostat. This leads to the change in potential at each ends of resistor AB , which is recorded by the voltmeter. In this way six sets of reading are taken from the ammeter and voltmeter .

The ratio of the potential difference and the current for each reading is found to be constant that is:

$\frac{V_{1}}{I_{1} } = \frac{ V_{2} }{ I_{2} } = \frac{ V_{3} }{ I_{3}} = \frac{ V_{4}}{ I_{4} } = \frac{ V_{5}}{ I_{5} } = \frac{ V_{6} }{ I_{6} } = constant \\ thus \: \frac{V}{I} = constant \: R \\ where \: R \: is\: the \:magnitude \: of \: resistance \\ or \: I = \frac{V}{R}$

Hence, Ohm's Law is proved.