Question

derive the formula of series and parallel resistances

Answer 1

Answer:

In series combination, resister are connected end to end and current has a single path through the circuit but the potential difference varies across each resistor. Thus we can write as,

V = V1 + V2 + V3

according to Ohm's law V = IR So,  

V1 = I R1, V2 = I R2, V3 = I R3

V = I R1 + I R2 + I R3

V = I(R1+R2+R3)

V =IRe

All the individual resistances become equal to the equivalent resistance.

​or Re = R1 + R2 + R3......Rn

In parallel combination, each resistor'sone is connected to the positive terminal while the other end is connected to a negative terminal. The potential difference across each resistance is the same and the current passing through them is different.

V = V1 =V2=V3

I  = I1+ I2+I3

Current throught each resistor will be:

I1= V/R1 , I2 = V/R2 = I3 = V/R3

I = V (1/R1+ 1/R2+1/R3)  

In case of equivalent resistance I=V/Re

V/Re =  V (1/R1+ 1/R2+1/R3)

So the equivalnet resistance is the sum of all resistances

   1/Re = 1/R1+ 1/R2+1/R3

Answer 2

derivation of series

let R1,R2,R3 be three resistors combined in series with a p.d( V )and current passing through it be( I)

V1=I*R1

V2=I*R2

V3=I*R3

-------------------------

(V1+V2+V3)=I(R1+R2+R3)

replacing V1,V2,V3 by (V)

V/I=R1+R2+R3

Req=R1+R2+R3

prooved

derivation of parallel resistance

let R1,R2,R3 be three resistances connected in parallel with a p.d( V)

I1=V/R1

I2=V/R2

I3=V/R3

--------------------

I1+I2+I3=V/R1+V/R2+V/R3

replacing I1+I2+I3 by I

I=V(1/R1+1/R2+1/R3)

I/V= 1/R1+1/R2+1/R3

1/V/I=1/R1+1/R2+1/R3

1/Req= 1/R1+1/R2+1/R3

prooved