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

Answer:

482853.39714 A/m²

$3.55\times 10^{-5}\ m/s$

Explanation:

I = Current = 2.54 A

d = Diameter = 2.588 mm

r = Radius = $\frac{d}{2}=\frac{2.588}{2}=1.294\ mm$

A = Area = $\pi r^2$

n = Charge density = $8.48\times 10^{28}\ electrons/m^3$

q = Charge of electron = $1.6\times 10^{-19}\ C$

Current density

$J=\frac{I}{A}\\\Rightarrow J=\frac{2.54}{\pi (1.294\times 10^{-3})^2}\\\Rightarrow J=482853.39714\ A/m^2$

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

Drift velocity

$v_d=\frac{I}{nqA}$

$I=JA$

$\\\Rightarrow v_d=\frac{J}{nq}\\\Rightarrow v_d=\frac{482853.39714}{8.48\times 10^{28}\times 1.6\times 10^{-19}}\\\Rightarrow v_d=3.55\times 10^{-5}\ m/s$

The drift velocity magnitude is $3.55\times 10^{-5}\ m/s$