Question

Derivation of formula of resistor connected in series and parallel

Answer 1

for series

take 3 resistors R1, R2 and R3 connected in series and a battery of V volts has been connected. suppose the p.d across R1 is V1, R2 is V2 and R3 is V3.

total p.d across the 3 resistors should be equal to the voltage of the battery i.e.

V = V1 + V2 + V3 __________[1]

from ohm 's law--

V = IR ___________[2]

V1 = IR1 _________[3]

V2 = IR2 _________[4]

V3 = IR3 _________[5]

putting values of V1, V2 and V3 in [1]

IR = IR1 + IR2 + IR3

=IR = I [R1 + R2 + R3]

=R = R1 + R2 +R3

for parellel--

take 3 resistors R1, R2, R3 connected in parellel and connect a batery of V volts. in this case the p.d across the ends will be the same. the current flowing, however, is not the same.

total I = I1 + I2 + I3 _______[1]

from ohm 's law--

I = V / R _______[2]

I1 = V / R1 _________[3]

I2 = V / R2 __________[4]

I3 = V / R3 _________[5]

putting the values of I1, I2 and I3 in [1]

V / R = V / R1 + V / R2 + V / R3

= V / R = V [1 / R1 + 1 / R2 + 1 / R3]

= 1 / R = 1 / R1 + 1 / R2 +1 / R3