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Derive an expression for the effective resistance when three resistors are connected in (i) series (ii) parallel

Derive an expression for the effective resistance when three resistors are connected in (i) series (ii) parallel

Grade:Upto college level

1 Answers

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
7 years ago
  1. Series
when three resisters are in series = the current passing through each is the same and the potential differs
let the three resistances beR_{1},R_{2}andR_{3}.
so
V_{1}=IR_{1}
V_{2}=IR_{2}
V_{3}=IR_{3}
the total pot isV=V_{1}+V_{2}+V_{3}
IR=IR_{1}+IR_{2}+IR_{3}
so
R=R_{1}+R_{2}+R_{3}
  1. Parallel
when the arrangement is parallel, the potential difference across each resistance remains the same only the current varies
so
I_{1}=V/R_{1}
I_{2}=V/R_{2}
I_{3}=V/R_{3}
also
I=I_{1}+I_{2}+I_{3}
V/R_{eq}=V/R_{1}+V/R_{2}+V/R_{3}
So
1/R_{eq}=1/R_{1}+1/R_{2}+1/R_{3}
Thanks and Regards
Apoorva Arora
IIT Roorkee
askIITians Faculty

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