A theostat has `1000` turn a wire radius `0.4 mm` having resistivity `49xx 10^(-8) Omega m`. The diameter of each turn is `4 cm. What are the maximum value of conductance and conductivity of rheostat wire.

Answer

`8.2 xx 10^(-3)S,2.04 xx 10^(6)S m^(-3)`

Explanation

Length of the wire used, `l = 1000 pi D`
Conductance, `G = (1)/(R) = (pi r^(2))/(rhol) = (pi r^(2))/(rho xx 1000 pi D)`
`= (r^(2))/(1000rhoD) = ((0.4 xx 10^(-3))^(2))/(1000 xx (49 xx 10^(-8)) xx (4 xx 10^(-2)))`
` = 8.2 xx 10^(-3)S`
Conductivity, `sigma = (1)/(rho) = (1)/(49 xx 10^(-8))`
`= 2.04 xx 10^(6)S m^(-1)`