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CBSE Class 10 Answered

what happens to the resistance of a conductor when (a) length is doubled  (b) area is doubled (c) length doubled and area is halved  (d) radius is doubled (e) diameteris doubled
Asked by vamsi14102003 | 22 May, 2018, 10:58: AM
answered-by-expert Expert Answer
The resistance of conductor (wire) R is given by,
R equals fraction numerator rho L over denominator A end fraction w h e r e comma space R minus R e s i s tan c e space o f space c o n d u c t o r L minus space l e n g t h space o f space c o n d u c t o r rho minus space r e s i s t i v i t y A minus space A r e a space o f space c r o s s space s e c t i o n
 
a) If length is doubled 
 
R equals fraction numerator rho left parenthesis 2 L right parenthesis over denominator A end fraction R equals 2 open parentheses fraction numerator rho L over denominator A end fraction close parentheses
If length is doubled resistance is doubled.
 
b) Area is doubled 
R equals fraction numerator rho L over denominator 2 A end fraction R equals 1 half open parentheses fraction numerator rho L over denominator A end fraction close parentheses
If area is doubled, resistance gets halved.
 
c) If length is doubled and area is halved
R equals fraction numerator rho left parenthesis 2 L right parenthesis over denominator begin display style A over 2 end style end fraction R equals 4 open parentheses fraction numerator rho L over denominator A end fraction close parentheses
If length is doubled and area is halved, resistance is 4 times that of original resistance 
 
d) Radius is doubled
 
A equals pi r squared R equals fraction numerator rho L over denominator pi left parenthesis 2 r right parenthesis squared end fraction space R equals fraction numerator rho L over denominator 4 pi r squared end fraction space T h u s comma space R equals 1 fourth open parentheses fraction numerator rho L over denominator A end fraction close parentheses
Thus, if radius is doubled , resistance becomes 1/4 times the original
 
e) Diameter is doubled
 
A equals space pi open parentheses d over 2 close parentheses squared R equals space fraction numerator rho L over denominator pi open parentheses fraction numerator 2 d over denominator 2 end fraction close parentheses squared end fraction R equals space fraction numerator rho L over denominator pi open parentheses d close parentheses squared end fraction d equals 2 r T h u s comma space R equals space fraction numerator rho L over denominator 4 pi r squared end fraction equals 1 fourth open parentheses fraction numerator rho L over denominator A end fraction close parentheses
 
If diameter is doubled, resistance becomes 1/4 times the original resistance.  
Answered by Shiwani Sawant | 22 May, 2018, 12:13: PM

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