When length of a conductor is decreased 10times. What will happen it's resistance.

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Solution

$D e a r S t u d e n t, W e k n o w r e s i s \tan c e o f a c o n d u c t o r i s, R = ρ \frac{l}{A} . . . . . . . . (1) l \to L e n g t h o f t h e c o n d u c t o r A \to A r e a o f c r o s s s e t i o n . ρ \to R e s i s t i v i t y o f t h e c o n d u c t o r . L e n g t h i s d e c r e a s e d 10 t i m e s . B u t v o l u m e o f t h e w i r e w i l l r e m a i n t h e s a m e . V o l u m e o f t h e w i r e i s, V = A l \Rightarrow F i n a l v o l u m e = i n i t i a l v o l u m e A_{f} l_{f} = A l A_{f} \frac{l}{10} = A l A_{f} = \frac{10}{l} \times A l = 10 A N e w r e s i s \tan c e i s, R_{n e w} = ρ \frac{l_{f}}{A_{f}} = ρ \frac{\frac{l}{10}}{10 A} = ρ \frac{l}{100 A} \Rightarrow R_{n e w} = \frac{1}{100} \times ρ \frac{l}{A} = \frac{1}{100} \times R (F r o m e q u a t i o n 1) R e s i s \tan c e i s d e c r e a s e d 100 t i m e s a s t h a t o f t h e i n i t i a l v a l u e . R e g a r d s .$

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