Question

There are n similar conductors each of resistance R. The resultant resistance comes out to be x when connected in parallel. If they are connected in series, the resistance comes out to be ________ .

Answer 1

Solution :

Given :-

n similar conductors each of resistance R are connected in parallel. Equivalent resistance of parallel connection is X

To Find :-

Equivalent resistance of n resistors when they are connected in series connection. (in terms of x)

Concept :-

▪ Equivalent resistance of n resistors which are connected in series is given by

$\underline{\boxed{\bf{\pink{R_{s}=R_1+R_2+.....+R_n}}}}$

▪ Equivalent resistance of n resistors which are connected in parallel is given by

$\underline{\boxed{\bf{\purple{\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+.....+\dfrac{1}{R_n}}}}}$

Calculation :-

$\implies\sf\:\dfrac{1}{R_p}=\dfrac{1}{R}+\dfrac{1}{R}+...n\:times\\ \\ \implies\sf\:\dfrac{1}{X}=\dfrac{n}{R}\\ \\ \implies\sf\:X=\dfrac{R}{n}\\ \\ \implies\boxed{\green{\bf{R=nX}}}\\ \\ \mapsto\sf\:R_s=R+R+...n\:times\\ \\ \mapsto\sf\:R_s=nR\\ \\ \mapsto\sf\:R_s=n(nX)\\ \\ \mapsto\underline{\boxed{\bf{\orange{R_s=n^2X}}}}$

Answer 2

Answer : Rs = n ^2X

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