Resistance of wire having radius r is R. If new wire of radius 2r, is made, then the new resistance of wire = ......

Options

A. `(R)/(2)`
B. `(R)/(16)`
C. 2R
D. 4R

Answer

B

Explanation

`(R)/(16)`
` R = (rho l)/(A) = (rho l A)/(A^(2)) = (rho V)/(pi^(2) r^(4))`
`therefore R prop (1)/(r^(4))`
`therefore (R_(1))/(R_(2)) = ((r_(1))/(r_(2)) )^(4)`
` (R^(2))/(R) = ((r)/(2r) )^(4) = ((1)/(16))`
`therefore R_(2) = (R)/(16)`