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Current and Drift Velocity

Sole the cont...

Question

Sole the contradiction in the following statements. 1) For a given conductor current does not change with cross sectional area. Whereas, 2) We have the formula i=n.e.A.v_d, wherein the charge e, drift velocity v_d and 'n' i.e. electron density is constant for a material. This implies that 'i' is directly proportional to 'A' i.e. area of cross section. This contradicts with the first statement. Explain.

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Solution

Dear student
$A s w e k n o w t h a t c u r r e n t i s t h e r a t e o f f l o w o f c h a r g e t h r o u g h a c r o s s s e c t i o n a l a r e a s o i f c u r r e n t t h r o u g h d i f f e r e n t c r o s s s e c t i o n a l a r e a i s n o t s a m e t h a n i t w o u l d l e a d t o t h e a c c u m u l a t i o n o f c h a r g e . I n t h e g i v e n r e l a t i o n i = n e A v_{d} i n f a c t t h e d r i f t v e l o c i t y c h a n g e s i t s v a l u e s o t h a t A v_{d} r e m a i n s c o n s \tan t t h r o u g h a n y a r e a o f c r o s s s e c t i o n . S o d r i f t v e l o c i t y i s l e s s w h e r e a r e a o f c r o s s s e c t i o n i s l e s s a n d v i c e v e r s a R e g a r d s$

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