Question

Prove that
$\bf \: v = ir$
​

Answer 1

Answer:

According to ohm's law -

At a constant temperature , when current is passes through a conductor is directly proportional to the potential difference across It ends.

V ∞ I

V = IR

V= I

R

Answer 2

WE KNOW,

$\huge \sf V \propto I \: \: \: \rm \{Ohm's \: \: law \}\\\tiny{ \rm \{dividing \: both \: sides \: by \:\gray{I} \} } \\ \\ \huge \sf \frac{V}{I} \propto \frac{I}{I} \\ \\ \\ \huge \sf \frac{V}{I} = k(constant) \times 1 \\ \\ \\ \huge \sf \frac{V}{I} = constant \\ \\ \tiny{ {\bf \{Here, \: constant \: value \: is \:R \: } \: \: { i.e.} \: \: \bf Resistance \: of \: conductor\} }\\ \\ \huge \sf \frac{V}{I} = R \\ \tiny{ \rm \{multiplying \: both \: sides \: by \:\gray{I} \} } \\ \\ \huge \sf \frac{V}{I} \times I = R\times I \\\tiny{ \rm \{\gray{I} \: gets \: cancelled \: in \: LHS \}} \\ \\ \huge \sf V = IR \: \: \: \: \tt_{\tiny{Proved!!}}$