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Derive the equation for equivalent resistance of a number of resisters connected in series
Asked by sonalivar | 31 Aug, 2018, 08:08: PM
answered-by-expert Expert Answer
 
Let resistances R1, R2 and R3 are connected in series as shown in figure.
This series combination is connected across a battery of emf V volts.
Let i be the current in the circuit. If Req is the equivalent resistance of this series combination, then we have
 
V = i×Req ........................................(1)
Let V1, V2 and V3 are potential differences across resistances R1, R2 and R3 respectively.
 
then we have,  V1 = i×R1 ............................(2)
                         V2 = i×R2 ............................(3)
                         V3 = i×R3 ............................(4)
sum of all potential differences V1, V2 and V3 should be equal to emf V of battery
 
V = V1+V2+V3 ...........................(5)
 
Using eqns.(1), (2), (3) and (4) we rewrite eqn.(5) as   i×Req = i×R1 + i×R2 + i×R3 .........(6)
 
eqn.(6) is simplified to give equivalent resistance as , Req = R1+R2+R3
Answered by Thiyagarajan K | 02 Sep, 2018, 07:02: PM

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