An aluminium wire of diameter 2.5 mm is connectedf in series with a copper wire of diameter1.6 mm. A current of 2.0 A is passed through them. Find (a) current density in aluminium wire, (b) drift velocity of electrons in copper wire. Given the number density of conduction electrons in copper is `10^(29) m^(-3)`.

Explanation

For A1, `r_(1)=2.5/2 mm =1.25 mm`
`= 1.25 xx 10^(3) m , I=2.0A`
Area of cross- section, `A_(1) = pi r_(1)^(2)`
`=3.14 (1.25 xx10^(-3))^(2)=4.9 xx 10^(-6) m^(2)`
For Cu, `r_(2)=1.6/2=0.8 mm=0.8xx10^(-3) m` ,
`n=10^(29) m^(-3)`
Area of cross-section, `A_(2)=pi r_(2)^(2)`
`=3.14(0.8 xx10^(-3))^(2)=2.01xx10^(-6) m^(2)`
(a) Current density in aluminium wire,
`J=I/A_(1)=2/(4.9xx10^(-6))=4.08 xx10^(5) A m^(-2)`
(b) Drift velocity in copper wire,
`v_(d)=(I)/("ne" A_(2))=2.0/(10^(29) xx 1.6 xx 10^(-19)xx2.01xx10^(-6))`
`=6.2 xx10^(-5) ms^(-1)`