A wire of silver has a resistance of 1 ohm. Specific resistance of constantan is 30 times the specific resistance of silver. Find the resistance of a constantan wire whose length is one third length of the silver wire and radius half the radius of the silver wire.

Explanation

`R_s = 1 Omega, rho_C = 30 rho_s`
Resistance of constantan `R_C =?`
Length `l_c =(l_s)/(3)`
radius `r_s = 2r_c`
We know that `R=(rhol)/(a) = (rhol)/(pir^2)`
`(R_c)/(R_s) = (rho_c)/(rho_s) (l_c)/(l_s) ((r_s)/(r_c))^2 = (30)/(3) xx 4 = 40`
Resistance of constantan `R_c = 40 xx 1 = 40 Omega`