what is ohm's law ? derive equivalent resistance for parallel and series connection of resistors.

 Dear Student ,
Ohm's Law is defined as:"The current through a conductor is directly proportional to the potential difference across it provided the temperature and other physical conditions remain constant".
Consider two resistors R₁ and R₂ are connected in series. the charge which moves out from resistor R1
be entering R₂. so the same value of current flows through R₁ and R₂.
potential difference across R₁ =V₁ =IR₁ -------(i)
potential difference across R₂  = V₂ = IR_{2         (ii)} 
the potential difference across the combination V = V₁+V₂.-----(iii)
By putting the values of (i), (ii) in equations (iii) we get
IReq =IR₁ +IR₂ = I(R₁+R₂) 

Req = R₁ +R_{2-----------------(iV)}

consider now the parallel combination of two resistors. the charge that flows  in A at from the left
flows out partly through R₁ and partly flow through R₂. so the value of currents are the rates of flow of charge at the point I = I₁+I₂
the potential difference between A and B is given by ohm's law applied to R1
V =I₁R_1,
I₁ = V/R₁
I₂= V/R₂
let Req be the equivalent resistance of combination

​$$\begin{gathered} \frac{V}{R_{eq}} =\frac{V}{R_1}+\frac{V}{R_2} \\ \frac{1}{Req}=\frac{1}{R1}+\frac{1}{R_2} \end{gathered}$$

Regards