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General Physics> Derive an expression for the effective re...

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

palash singh , 11 Years ago

Grade Upto college level

1 Answers

Apoorva Arora

Last Activity: 10 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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