Question

An 18 gauge copper wire (the size usually used for lamp cords), with a diameter of 1.02 mm,1.02 mm, carries a constant current of 1.67 A1.67 A to a 200 W lamp. The free-electron density in the wire is 8.5×10288.5×1028 per cubic meter. Find (a) the current density and (b) the drift speed.

Answer 1

Hey! How are you? My name is Maria, 19 years old. Yesterday broke up with a guy, looking for casual sex.

Write me here and I will give you my phone number - *pofsex.com*

My nickname - Lovely

Answer 2

Answer:

J = 2.044x10⁶ A/m²

v = 1.50x10⁻⁴ m/s

Explanation:  

The current density (J) of the copper wire is giving by:  

$J = \frac {I}{A}$

where I: electric current and A: cross-sectional area of the copper wire

The cross-sectional area of the copper wire can be calculated by:

$A = \frac {\pi d^{2}}{4} = \frac {\pi (1.02 \cdot 10^{-3} m)^{2}}{4} = 8.17 \cdot 10^{-07} m^{2}$         

Substituting the calculated area in the equation (1) we have:

$J = \frac {1.67 A}{8.17 \cdot 10^{-7} m^{2}} = 2.044 \cdot 10^{6} \frac {A}{m^{2}}$    

Hence, the current density is 2.044x10⁶ A/m².    

To find the drift speed (v), we need to use the next equation:

$v = \frac {J}{n q}$  

where n: the free-electron density, q: module of the charge of the electron

$v = \frac {2.044 \cdot 10^{6} \frac {A}{m^{2}}}{(8.5 \cdot 10^{28} {m^{-3}}) (1.6 \cdot 10^{-19} C)}$  

$v = 1.50 \cdot 10^{-04} \frac {m}{s}$                            

So, the drift speed is 1.50x10⁻⁴ m/s.

Have a nice day!