Two wires made up of the same material and having the same length have diameters in the ratio 2:1. Which one of the wires will have a higher resistance?

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Solution

$R e s i s \tan c e i s d i r e c t l y p r o p o r t i o n a l t o t h e l e n g t h a n d i n v e r s e l y p r o p o r t i o n a l t o a r e a o f c r o s s s e t i o n o f a c o n d u c t o r . T h e r e l a t i o n i s : R = σ \frac{l}{A}, w h e r e l a n d A a r e l e n g t h a n d a r e a o f c r o s s s e c t i o n r e s p e c t i v e l y . A c c o r d i n g t o a b o v e r e l a t i o n m o r e t h e a r e a o f c r o s s s e c t i o n l e s s t h e r e s i s \tan c e a n d v i c e v e r s a . T h e a r e a o f s e c o n d w i r e i s l e s s, t h e r e f o r e i t s r e s i s \tan c e i s h i g h e r .$

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