Cross SeelomL 0.2 x 10-7 ?-m 3 x 107 ?-m 5x10-7 ?-m 2. a. Which way (on average)

Question

Cross SeelomL 0.2 x 10-7 ?-m 3 x 107 ?-m 5x10-7 ?-m 2. a. Which way (on average) are the free electrons in the conductor drifting b. es How many electrons cross the boundaries between the wire sections each second? Give 2 answers, one for each boundary c. What is the voltage drop across each section? d. What is the power dissipation of each section? e. The difference in power dissipation causes a temperature gradient along the length of the middle wire. The temperature varies with location in a linear fashion from 25°C to 35°C following T(x) 25°C10x where the left side of the middle wire is the origin x=0 m. The resistivity depends on temperature according to the formula ?(T) = (3×1070m) + 10-8 Am (T- 25°C). What is the resistance of this middle section taking this thermal effect into account?

Explanation / Answer

a)The electrons are drifting into left direction and hence current flows in right direction.

b)We know from the defination of current

I = Q/t = nQ/t

n = I/Q = (23 x 10^-3)/(1.6 x 10^-19) = 1.44 x 10^16 electrons/s

Hence, n = 1.44 x 10^16 electrons/s

c)We know that,

R = rho L/A

R1 = 0.2 x 10^-7 x 0.5/(1 x 10^-6) = 0.01 Ohm

V = IR

V1 = 23 x 10^-3 x 0.01 = 23 x 10^-5 V

R2 = 3 x 10^-7 x 1/(1 x 10^-6) = 0.3

V2 = 23 x 10^-3 x 0.3 = 6.9 x 10^-4 V

R3 = 5 x 10^-7 x 0.5/(1 x 10^-6) = 0.25

V3 = 23 x 10^-3 x 0.25 = 5.75 x 10^-3 V

d)P = I^2 R

P1 = (23 x 10^-3)^2 0.01 = 5.29 x 10^-6 W

P2 = (23 x 10^-3)^2 0.3 = 1.59 x 10^-4 W

P3 = (23 x 10^-3)^2 0.25 = 1.32 x 10^-4 W

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