A piece of wire of resistance20Ω is drawn out so that

A piece of wire of resistance20Ω is drawn out so that
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 A piece of wire of resistance20Ω is drawn out so that its length is increased to twice its original length.
calculate the resistance of the wire in the new situation.
 

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SOLUTION

R equals 20 space capital omega L e t comma space L e n g t h space o f space w i r e space i s space L space a n d space w h e n space i t space d r a w n space o u t comma space i t s space n e w space l e n g t h space i s space 2 L T h e space v o l u m e space o f space w i r e space i n space b o t h space t h e space s i t u a t i o n s space r e m a i n s space c o n s tan t. S o comma space i t space t h e space l e n g t h space o f space w i r e space d o u b l e d comma space t h e space a r e a space o f space c r o s s space s e c t i o n space o f space w i r e space b e c o m e s space h a l f. S o comma space t h e space n e w space r e s i s tan c e space o f space w i r e minus R subscript n e w end subscript space equals rho fraction numerator space 2 L over denominator begin display style bevelled A over 2 end style end fraction R subscript n e w end subscript space equals space rho fraction numerator 4 L over denominator A end fraction R subscript n e w end subscript space equals space 4 cross times O l d space r e s i s tan c e space o f space w i r e space space space space space space space space space space space left parenthesis B e c a u s e comma space R equals rho L over A right parenthesis R subscript n e w end subscript space equals 80 space capital omega

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