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
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](https://images.topperlearning.com/topper/tinymce/cache/981dd17de62a1075359c47c898e4e099.png)
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](https://images.topperlearning.com/topper/tinymce/cache/b96502d7479c1c846682467ed3fc6e42.png)
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](https://images.topperlearning.com/topper/tinymce/cache/92ed6360a8a2e88f7034a374b694f2ba.png)
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](https://images.topperlearning.com/topper/tinymce/cache/37b62f6a5a6bcd785cb7f32ae475ae34.png)
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](https://images.topperlearning.com/topper/tinymce/cache/6bb9bdc0c4fe63ceb95fb5d53cb1643e.png)
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](https://images.topperlearning.com/topper/tinymce/cache/126f2fdb568ad45454a6ed9d15f0ec02.png)
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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