deduce the expression for equivalent resistance of the parallel combination of resistors R1, R2, R3
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Answer:
r = r1 + r2 + r3
Explanation:
take 3 resistors r1, r2, r3 connected in parallel and connect a battery 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
I hope it will help you
regards
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