A wire of resistance R is stretched so that its radius decreases by factor n. Calculate its new resistance.
The volume of the wire should remain constant.?
V = pi r^2 L?
If the radius decreases by a factor of n, the length must increase by a factor of n^2 to keep the volume constant.?
V = pi (r/n)^2 (n^2 L)?
The formula for resistance is?
R = p L/A = p L/(pi r^2)?
Increase L by n^2 and decrease r by n:?
R_new = p (n^2 L)/(pi (r/n)^2) = n^4 p L/A = n^4 R?
Its new resistance is n^4 times the old.
V = pi r^2 L?
If the radius decreases by a factor of n, the length must increase by a factor of n^2 to keep the volume constant.?
V = pi (r/n)^2 (n^2 L)?
The formula for resistance is?
R = p L/A = p L/(pi r^2)?
Increase L by n^2 and decrease r by n:?
R_new = p (n^2 L)/(pi (r/n)^2) = n^4 p L/A = n^4 R?
Its new resistance is n^4 times the old.