Q: Calculate the current density $$J in $$the cylindrical section (diameter $$1\ \mathrm{cm}) if $$the current is $$20\ \mathrm{A}.$$

$$2.55 \times 10$$^{5}$$\ \mathrm{A/m}^2$$

Q: If the current density in the block section is $$8.89 \times 10$$^{4}$$\ \mathrm{A/m}^2$$, what is the drift velocity of electrons in this section? (Use $$n = 8.5 \times 10$$^{28}$$\ \mathrm{m}^{-3}$$ and $$e = 1.6 \times 10$$^{-19}$$\ \mathrm{C})$$

$$6.5 \times 10$$^{-5}$$\ \mathrm{m/s}$$

Q: If the conductivity of copper is $$6 \times 10^7$\ \mathrm{S/m}$$, what is the electric field in the rod section where $$J = 2.55 \times 10^5$\ \mathrm{A/m}^2$$?

$$4.25 \times 10$$^{-3}$$\ \mathrm{V/m}$$

Q: If the number of conduction electrons in the slab section is $$2 \times 10$$^{23}$$, what is the volume of the slab? (Use n = 8.5$$ \times $$10^{28}$$\ \mathrm{m}^{-3}$$)

$$2.35 \times 10$$^{-6}$$\ \mathrm{m}^3$$

Q: A copper conductor is shaped into a rod with a diameter of $$1\ \mathrm{cm}$$ and length $$3\ \mathrm{cm}. If $$the current is $$20\ \mathrm{A}$$, what is the cross-sectional area of the rod?

$$7.85 \times 10$$^{-5}$$\ \mathrm{m}^2$$

Question 1

A copper conductor consists of three sections: a 3 cm-long block with a 1.5 cm × 1.5 cm square cross-section, a 3 cm-long cylinder with a 1 cm diameter, and a plate 6 cm × 4 cm × 1 cm thick. If a current of 20 A flows through the conductor, what is the current through the cylindrical section?

Accepted Answer

$$20\ \mathrm{A}$$

Question 2

Given the number density of conduction electrons in copper is $$8.5 	imes 10$$^{28}$$\ \mathrm{m}^{-3}$$, what is the total number of conduction electrons in the block section (3 cm long, 1.5 cm × 1.5 cm cross-section)?

Accepted Answer

$$5.7 	imes 10$$^{23}$$

Question 3

What is the formula for current density $$J in $$terms of current $$I$$ and cross-sectional area $$A$$?

Accepted Answer

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

Question 4

Calculate the current density $$J in $$the cylindrical section (diameter $$1\ \mathrm{cm}) if $$the current is $$20\ \mathrm{A}.$$

Accepted Answer

$$2.55 	imes 10$$^{5}$$\ \mathrm{A/m}^2$$

Question 5

Which of the following best explains why the current is the same through all three sections of the copper conductor?

Accepted Answer

Current is conserved in a series circuit, so the same current must flow through each section.

Question 6

Given the formula for drift velocity $$v_d as$$ $$v_d = \frac{J}{n e}$$, where $$J is $$current density, $$n is $$the number density of electrons, and $$e is $$the elementary charge, which of the following correctly expresses $$v_d$$?

Accepted Answer

$$v_d = \frac{J}{n e}$$

Question 7

If the current density in the block section is $$8.89 	imes 10$$^{4}$$\ \mathrm{A/m}^2$$, what is the drift velocity of electrons in this section? (Use $$n = 8.5 	imes 10$$^{28}$$\ \mathrm{m}^{-3}$$ and $$e = 1.6 	imes 10$$^{-19}$$\ \mathrm{C})$$

Accepted Answer

$$6.5 	imes 10$$^{-5}$$\ \mathrm{m/s}$$

Question 8

Which equation relates the electric field $$E in a $$conductor to the current density $$J$$ and the conductivity $$\sigma$$?

Accepted Answer

$$E = \frac{J}{\sigma}$$

Question 9

If the conductivity of copper is $$6 	imes 10^7$\ \mathrm{S/m}$$, what is the electric field in the rod section where $$J = 2.55 	imes 10^5$\ \mathrm{A/m}^2$$?

Accepted Answer

$$4.25 	imes 10$$^{-3}$$\ \mathrm{V/m}$$

Question 10

A student claims that increasing the cross-sectional area of a conductor while keeping the current constant will increase the drift velocity of electrons. Is this correct?

Accepted Answer

No, increasing the area decreases the current density and thus decreases the drift velocity.

Question 11

If the number of conduction electrons in the slab section is $$2 	imes 10$$^{23}$$, what is the volume of the slab? (Use n = 8.5$$ 	imes $$10^{28}$$\ \mathrm{m}^{-3}$$)

Accepted Answer

$$2.35 	imes 10$$^{-6}$$\ \mathrm{m}^3$$

Question 12

Which of the following best describes the relationship between current density and electric field in a conductor?

Accepted Answer

Current density is directly proportional to the electric field, with conductivity as the proportionality constant.

Question 13

A copper wire and an aluminum wire of the same length and cross-sectional area carry the same current. Which has the higher drift velocity of electrons, and why?

Accepted Answer

Aluminum, because it has a lower number density of conduction electrons.

Question 14

If the drift velocity in the rod section is $$1.88 	imes 10$$^{-4}$$\ \mathrm{m/s}$$, what would happen to the drift velocity if the current were doubled, all else held constant?

Accepted Answer

It would double.

Question 15

Which of the following is a correct expression for the electron current $$I_e in $$terms of the number of electrons $$N_e$$, elementary charge $$e$$, and time $$t$$?

Accepted Answer

$$I_e = \frac{N_e e}{t}$$

Question 16

A copper conductor is shaped into a rod with a diameter of $$1\ \mathrm{cm}$$ and length $$3\ \mathrm{cm}. If $$the current is $$20\ \mathrm{A}$$, what is the cross-sectional area of the rod?

Accepted Answer

$$7.85 	imes 10$$^{-5}$$\ \mathrm{m}^2$$

Current, Current Density, and Drift Velocity in a Composite Copper Conductor

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