Three resistances rı, r2 and r3 joined in parallel. Draw circuit diagram and
derive expression for equivalent resistance.
Answers
Answer:
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