Derive an expression for the effective resistance when three resistors connected in (1) series (2) parallel || Series Combination || Parallel Combination

*** Derive an expression for the effective resistance when three resistors connected in (1) series (2) parallel.

(1) Series Combination :-

*  When the resistance are connected end to end is called series Combination.

* In Series Combination current remains Same potential divides.

* Let us consider three resistors R1, R2,R3 are connected in series with help of battery of potential weak.
* In series Combination of resistors potential divides current remains Same.
        
               ::  V = V1+V2+V3

According to Ohm's law

V = V1+ V2+ V3
iR = iR1 + iR2+ iR3
iR = i ( R1+R2+R3 )
Re = R1+R2+R3 

*** It Means effective resistance is equal to sum of individual resistances.

Note :-  If " n " Identical no.of resistors are connected in series.
Re= R + R + R...........
Re = nR

(2) Parallel Combination :-

* All the first ends of the resistance are connected to one Terminal, All the second ends are connected to another terminal finally these are connected by the battery is called Parallel Combination.

* In this potential same current divides.

* Let us consider three resisterce R1, R2 and R3 are connected in parallel with a battery of potential V.

* In these current divides, potential same.
                 i = i1 + i2 + i3

According to Ohm's law

i = V/R
i1 = V/R1
i2 = V/R2
i3 = V/R3

i = i1 + i2 + i 3
V/R = V/R1 + V/R2 + V/R3
V/R = V( 1/R1 + 1/R2 + 1/R3 )
1/Re = 1/R1 + 1/R2 + 1/R3

* The reciprocal effective of resistance is equal to sum of reciprocal individual resisterce.

Note :-  When " n " Identical no.of resistors are connected in parallel.
1/Re = 1/R + 1/R + 1/R......
1/Re = n/R
Re = R/n