Answer to Question #307494 in Electric Circuits for Ash

Question

1. Find the current density and drift velocity of free electrons when the particles travel on a copper conductor with a square cross-section of 1.0 mm on the side and carries a current of 40 A to a 5 hp electric meter and its density of 6.0 x 1028 electrons/m3

2. Suppose the resistance is 1.47 Ω at a temperature of 20°C. Find the resistance at 0 degree Celsius.

Answer 1

Solution:

$1. a=1\sdot10^{-3}m;$

$I=40A;$

$n=6.0\sdot10^{28}m^{-3};$

$j=\dfrac{I}{A};$

$A=a^2=1\sdot10^{-6}m^2;$

$j=\dfrac{40}{1\sdot10^{-6}}=40\sdot 10^6A/m^2;$

$v_d=\dfrac{I}{neA};$

$v_d=\dfrac{40}{6.0\sdot10^{28}\sdot1.6\sdot10^{-19}\sdot 1\sdot10^{-6}}=4.17\sdot10^{-3} m/s;$

$2. R=1.47\Omega;$

$T=20^oC;$

$T_0=0^oC;$

$\alpha=0.0043;$

$R_0-?;$

$R=R_0(1+\alpha\Delta T)$ ;

$R_0=\dfrac{R}{1+\alpha \Delta T};$

$R_0=\dfrac{1.47}{1+0.0043\sdot20}=1.35\Omega;$

Answer:$1. j=40\sdot10^6 A/m^2; v_d=4.17\sdot10^{-3}m/s;$

$2. R_0=1.35\Omega.$