How is the resistance of a wire affected if a) Its length is doubled b) Its area is doubled c) Its radius is doubled
Answers
Explanation:
resistance= rho X length/area of cross-section
so, resistance is directly proportional to length and if the length is doubled the resistance gets doubled as well
b) resistance is inversely proportional to the area of cross-section so if area is doubled, the resistance is halved
c) R1=¶ l/2πr1
R2=¶ X l/2π2r1
or, R2=¶X l/4πr1
or, R2=(1/2)X R1
We know that,
R = p l/A
Here, R = resistance, p = rho (resistivity), l = length and A = area of cross section.
a) If length is doubled
l = 2l
So,
R = p (2l)/A
If the length of the wire is doubled then, resistance also becomes double.
( As resistance is directly proportional to length. So, with an increase in length resistance also increase. )
b) If the area is doubled
A = 2A
So,
R = p l/(2A)
R = 1/2 (pl)A
If the area is doubled then resistance gets halved of the original resistance.
( As resistance is inversely proportional to area. So, with an increase in area, the resistance of the wire decreases. )
c) If the radius is doubled
r = 2r
We know that A = πr²
R = p l/(πr²)
As r = 2r So, r² = 4r²
R = p l/π4r²)
R = 1/4 (pl)/(πr²)
R = 1/4 (pl)/A
If the radius of doubled then resistance becomes 4 times the original resistance.