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Grade Upto college level General Physics

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

palash singh

12 Years agoGrade Upto college level

1 Answer

Apoorva Arora

12 Years ago

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

$R=R_{1}+R_{2}+R_{3}$

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

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