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

Apoorva Arora IIT Roorkee
6 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 be$R_{1}$,$R_{2}$and$R_{3}$.
so
$V_{1}=IR_{1}$
$V_{2}=IR_{2}$
$V_{3}=IR_{3}$
the total pot is$V=V_{1}+V_{2}+V_{3}$
$IR=IR_{1}+IR_{2}+IR_{3}$
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