Ask Your Teacher A block in the shape of a rectangular solid has a cross-sectional area of 3.00 cm2 across its width, a front-to-rear length of 15.1 cm, and a resistance of 945 Ω. The block's material contains 5.33 ✕ 1022 conduction electrons/m3. A potential difference of 35.4 V is maintained between its front and rear faces. (a) What is the current in the block?

a. 37.5 mA b. 124.9 A/m² c. 1.46 cm/s d. 234.44 V/m

Explanation:

Here is the complete question

A block in the shape of a rectangular solid has a cross-sectional area of 3.00 cm2 across its width, a front-to-rear length of 15.1 cm, and a resistance of 945 Ω. The block's material contains 5.33 × 1022 conduction electrons/m3. A potential difference of 35.4 V is maintained between its front and rear faces. (a) What is the current in the block? (b) If the current density is uniform, what is its magnitude? What are (c) the drift velocity of the conduction electrons and (d) the magnitude of the electric field in the block?

Solution

a. The current in the block, I

I = V/R where V = potential difference between its front and rear faces = 35.4 V, R = resistance = 945 Ω

I = V/R = 35.4 V/945 Ω = 0.0375 A = 37.5 mA

b. The current density J

J = I/A  where A = cross-sectional area of block = 3.00 cm² = 3 × 10⁻⁴ m²

J = I/A = 0.0375 A /3 × 10⁻⁴ m² = 124.9 A/m²

c. The drift velocity of the electrons

From J = nev, v = J/ne where n = electron density = 5.33 × 10²² electrons/m³

e = electron charge = 1.602 × 10⁻¹⁹C

v = J/ne = 124.9 A/m²/(5.33 × 10²² electrons/m³ × 1.602 × 10⁻¹⁹C)

  = 0.0146 m/s = 1.46 cm/s

d. The magnitude of the electric field, E

E = V/L where V = potential difference applied between its front and rear ends = 35.4 V and L = front-to-rear length of block = 15.1 cm = 0.151 m

E = V/L = 35.4 V/0.151 m = 234.44 V/m

Explanation:

Given:

Cross-sectional area, A = 3.00 cm^2

Converting from cm^2 to m^2,

3 cm^2 × (1 m)^2/(100 cm)^2

= 3 × 10^-4 m^2

Length, L = 15.1 cm

Resistance, R = 945 Ω

N = 5.33 ✕ 10^22 conduction electrons/m^3

Potential difference, V = 35.4 V

A.

Using ohm's law,

Potential difference, V = current, I × resistance, R

I = 35.4/945

= 0.0375 A.

B.

Current density, J = I/A

= 0.0375/3 × 10^-4

= 124.87 A/m^2

carbon is found in all living things. carbon atoms move constantly through

living organisms, the oceans, the atmosphere, and the earth’s crust in what is

known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

tropical swamp forests. the trees and other

plants were immense and

provided an endless supply of

food for the giant animals that

roamed the land. somewhere in

the air above one of these

forests, a lone carbon atom has joined

up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

energy in the plant’s cells through photosynthesis. the oxygen (o2) from the

co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

different situation would have developed. let’s say

that a giant plant-eating dinosaur (herbivore) ate the

fern for breakfast, and swallowed the carbon in the

fern in the form of carbohydrates and proteins. in

the process of respiration, oxygen combined with

the carbohydrates and proteins in the dinosaur’s cells

to provide energy for its daily activity.