An object made of a material with resistivity of Pres =6 ohmm . The objects geom
ID: 1434172 • Letter: A
Question
An object made of a material with resistivity of Pres =6 ohmm . The objects geometry has a basic shape with a length L, width W, and height H. In addition to this, there is a rectangular blocks missing from the center of the geometry with dimensions L/3,W/3, and H which offers two different legs for current pass through(see figure). L = 1 cm, W = 1 cm, and H = 2 mm.
Please be clear and show all work
W/3/ l eg #1 W/3 / leg#2 L/3 L/3 L/3 a) What is the total resistance R of this object? b) If an electric potential of V 10 volts is applied across this structure, what is the current entering and leaving it? c) What is the current through one of the legs? If the electrons are moving at an average rate of 10 m/s, what is the charge density inside a leg? How does this compare with the charge density in the first part of the structure (assume the average velocity is the same in both sections)? d)Explanation / Answer
R = resistivity x length / cross sectional area
for left L/3:
RL = 6 x (L/3) / (W H) = 2 L / WH
RL = (2 x 0.01 ) / (0.01 x 0.002) = 1000 ohm
for leg 1:
R1 = 6 x (L/3) / (W/3 H) = 6 L / WH
R1 = (6x 0.01 ) / (0.01 x 0.002) = 3000 ohm
for leg2:
R2 = 6 x (L/3) / (W/3 H) = 6 L / WH
R2 = (2 x 0.01 ) / (0.01 x 0.002) = 3000 ohm
for right L/3:
Rr = 6 x (L/3) / (W H) = 2 L / WH
Rr = (2 x 0.01 ) / (0.01 x 0.002) = 1000 ohm
now R1 and R2 are in parallel hence equivalent of these two parts.
1/R' = 1/R1 + 1/R2 = 1/3000 + 1/3000 = 1/1500
R' = 1500 ohm
now R', RL and Rr are in series connection,
Req = R' + RL + Rr = 1500 + 1000 +1000 = 3500 ohm
b) I = V/Req = 10 / 3500 = 2.86 x 10^-3 A Or 2.86 mA
c) current through leg = I/2 = 1.43 x 10^-3 A or 1.43 mA
d) I = Q/t
electron travels 10 m per second.
time taken to travel 1/3 cm = (1/300 )m / 10 m/s = 3.33 x 10^-4 s
charge travels in this time = 1.43 x 10^-3 x 3.33 x 10^-4 = 4.77x 10^-7 C
no of electrons = (4.77 x 10^-7 ) / (1.6 x 10^-19) = 2.98 x 10^12 eelectrons
density = (2.98 x 10^12 ) / (0.01/3 x 0.01/3 x 0.001)
= 2.68 x 10^20 electrons / m^3
for first part = (5.96 x 10^12 ) / (0.01/3 x 0.01 x 0.001)
= 1.788 x 10^20 electrons / m^3