First slide

Resistors

Question

A wire of resistance ‘R’ is elongated n-fold to make a new uniform wire. The resistance of new wire

Easy

A

$nR$
B

$n^{2} R$
C

$2nR$
D

${2n}^{2} R$

Solution

$V o l u m e w i l l r e m a i n s a m e . l A = l^{'} A^{'} \Rightarrow l A = n l A^{'} \Rightarrow A' = \frac{A}{n} N o w t a k e r a t i o o f n e w a n d o l d v a l u e s o f r e s i s \tan c e s \frac{R'}{R} = \frac{(ρ l' / A')}{(ρ l / A)} = \frac{n l / (A / n)}{(l / A)} = n^{2} I I m e t h o d : I f w i r e i s e l o n g a t e d t h e n R \propto l^{2} \Rightarrow \frac{R'}{R} = {(\frac{l'}{l})}^{2} \Rightarrow R' = R {(\frac{n l}{l})}^{2} = n^{2} R$

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