Question

Write the expression for effective resistance in series combination and parallel combination resistors

Answer 1

Series combination

Re=R1+R2+R3.....Rn

Parallel combination

1/Re=1/R1+1/R2+1/R3....1/Rn

Answer 2

Given,

1)In series current is constant,

Let's assume we have 'n' number of resistors,

therefore,

V=$V_{1} +V_{2} +...+V_{n}$

IR = $IR_{1} +IR_{2} +....+IR_{n}$

R=$R_{1} +R_{2} +....+R_{n}$

2) In parallel voltage is constant,

Let's assume we have 'n' number of resistors,

therefore,

I =$I_{1} +I_{2} +...+I_{n}$

$\frac{V}{R} =\frac{V}{R_{1} } +\frac{V}{R_{2}} +...+\frac{V}{R_{n} }$

$\frac{1}{R} =\frac{1}{R_{1} } +\frac{1}{R_{2} } +....+\frac{1}{R_{n} }$

∴Hence the effective resistance in series combination is,

R=$R_{1} +R_{2} +....+R_{n}$

and in parallel combination resistors is,

$\frac{1}{R} =\frac{1}{R_{1} } +\frac{1}{R_{2} } +....+\frac{1}{R_{n} }$