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When 5 V potential difference is applied...

When 5 V potential difference is applied across a wire of length 0.1 m. The drift speed of electrons is `2.5 xx 10^(-4) ms^(-1)`. If the electron density in the wire is `8 xx10^(28) m^(-3)`, calculate the resistivity of the material of wire

Text Solution

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Here, `r = 6.0 mm = 6 xx 10^(-3)m`,
`l = 3.0 xx 10^(-2)m`,
`rho = 3.5 xx 10^(-5)Omega m , P = 2.0W`.
(a) As `P = I^(2)R = (JA)^(2)R = J^(2)A^(2)R`
Current density ,
`J = 1/A sqrt(P/R) = 1/A sqrt(P/(rho l//A)) = sqrt(P/(rho l//A)`
` = sqrt(2.0/((3.5xx10^(-5)) xx (3.0 xx 10^(-2)) xx pi xx (6 xx 10^(-3))^(2))`
` = 1.3 xx 10^(5)Am^(-2)`
(b) As `P = IV =JAV`
or `V = P/(AJ) = P/(pi r^(2)J)`
`20/(3.14 xx (6 xx 10^(-3))^(2)xx(1.3 xx 10^(5))`
`=0.136 V`
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