A wire P has resistance of 20 ohm. Another wire Q of same material but length twice that of P has resistance of 8 ohm. If r is the radius of cross-section of P, the radius of cross-section of Q is

Options

A. `r`
B. `(r )/(sqrt(2))`
C. `rsqrt(5)`
D. `2r`

Answer

C

Explanation

The wire P has resistance of `20Omega`. Let its length be l and radius `r therefore R_(P)=(rhol)/(pir^(2))" "...(i)`

The wire Q has resistance of `8Omega`. Let its length be 2l. Let the unknown radius be `r_(Q)`.
`R_(Q)=(rho2l)/(pir_(Q)^(2))" "...(ii)`<

Divide (i) by (ii) we get
`(R_(P))/(R_(Q))=(r_(Q)^(2))/(2r^(2))or(20)/(8)=(r_(Q)^(2))/(2r^(2))orr_(Q)^(2)=5r^(2)orr_(Q)=sqrt(5)r`