Question

Explain the Series and parallel combinations of resistors with the help of its equation.

Answer 1

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