Question

The current supplied to an air conditioner unit is 2.54 amps. The air conditioner is wired using a 10-gauge (diameter 2.588 mm) wire. The charge density is n = 8.48 ✕ 1028 electrons/m3.Find the following magnitudes.(a) current density (in A/m2)?(b)the drift velocity (in m/s)?

Answer 1

482853.39714 A/m²

`3.55* 10^(-5)\ m/s`

Step-by-step explanation:

I = Current = 2.54 A

d = Diameter = 2.588 mm

r = Radius =
`(d)/(2)=(2.588)/(2)=1.294\ mm`

A = Area =
`\pi r^2`

n = Charge density =
`8.48* 10^(28)\ electrons/m^3`

q = Charge of electron =
`1.6* 10^(-19)\ C`

Current density

`J=(I)/(A)\\\Rightarrow J=(2.54)/(\pi (1.294* 10^(-3))^2)\\\Rightarrow J=482853.39714\ A/m^2`

The current density is
`482853.39714\ A/m^2`

Drift velocity

`v_d=(I)/(nqA)`

`I=JA`

`\\\Rightarrow v_d=(J)/(nq)\\\Rightarrow v_d=(482853.39714)/(8.48* 10^(28)* 1.6* 10^(-19))\\\Rightarrow v_d=3.55* 10^(-5)\ m/s`

The drift velocity magnitude is
`3.55* 10^(-5)\ m/s`