Question

derive an expression for equivalent resistance for system of resistors when connected in (a) series (b) parallel

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Answer 1

In Series

$V=V_{1}+V_{2}+V_{3}   \\IR=IR_{1} +IR_{2} +IR_{3}   (Put V=IR) \\IR=I(R_{1}+R_{2}  +R_{3} )\\R=R_{1} +R_{2}+R_{3}$

In Parallel

$I=I_{1}+I_{2}  +I_{3}\\V/R=V/R_{1} +V/R_{2}+V/R_{3}   (Put I=V/R)\\V/R=V(1/R_{1} +1/R_{2}+1/R_{3})\\1/R=1/R_{1} +1/R_{2}+1/R_{3}$