Q: A copper wire has a cross-sectional area of $$3.3 \times 10$$^{-6}$$\ \mathrm{m}^2$$ and carries a current of $$10\ \mathrm{A}. $$The conduction electron density in copper is $$8.49 \times 10$$^{28}$$\ \mathrm{electrons/m}^3. $$What is the drift speed of the electrons in the wire?

$$2.2 \times 10$$^{-4}$$\ \mathrm{m/s}$$

Question 1

Which of the following best describes the conventional direction of electric current in a conductor?

Accepted Answer

The direction in which positive charges flow.

Question 2

A copper wire has a cross-sectional area of $$3.3 	imes 10$$^{-6}$$\ \mathrm{m}^2$$ and carries a current of $$10\ \mathrm{A}. $$The conduction electron density in copper is $$8.49 	imes 10$$^{28}$$\ \mathrm{electrons/m}^3. $$What is the drift speed of the electrons in the wire?

Accepted Answer

$$2.2 	imes 10$$^{-4}$$\ \mathrm{m/s}$$

Question 3

Which equation correctly relates current density $$\vec{J}$$, charge carrier density $$n$$, charge $$q$$, and drift velocity $$\vec{v}_d$$?

Accepted Answer

$$\vec{J} = n q \vec{v}_d$$

Question 4

A wire of length $$L$$ and cross-sectional area $$A is $$made of a material with resistivity $$\rho. $$What is the resistance $$R of $$the wire?

Accepted Answer

$$R = \rho \dfrac{L}{A}$$

Question 5

Which material would you expect to have the lowest resistivity at room temperature based on the provided table?

Accepted Answer

Silver

Question 6

A current of $$2\ \mathrm{A}$$ flows through a resistor with a resistance of $$5\ \Omega. $$What is the voltage across the resistor?

Accepted Answer

$$10\ \mathrm{V}$$

Question 7

If the temperature of a metal wire increases, what generally happens to its resistivity?

Accepted Answer

It increases.

Question 8

A solution of NaCl conducts electricity by the movement of Na$$^+$$ and Cl$$^-$$ ions. If $$n_1$$ and $$n_2$$ are the number densities, $$q_1$$ and $$q_2$$ are the charges, and $$v_1$$ and $$v_2$$ are the drift velocities of Na$$^+$$ and Cl$$^-$$, respectively, what is the total current $$I$$ through area $$A$$?

Accepted Answer

$$I = A(n_1$ q_1$ v_1$ + n_2$ q_2$ v_2$)$$

Question 9

Which of the following statements about Ohmic and non-Ohmic materials is correct?

Accepted Answer

Ohmic materials have a constant resistivity and a linear $$J vs$$. $$E$$ graph.

Question 10

A cylindrical resistor has a length $$L$$ and a radius $$r. If $$its resistivity at $$20^{\circ}$$\mathrm{C}$$ is $$\$$rho_0$$ and the temperature coefficient is $$\alpha$$, what is the resistivity $$\rho at $$temperature $$T$$?

Accepted Answer

$$\rho = \$$rho_0$$ (1 + \alpha (T - T_0$))$$

Question 11

A wire splits into two branches of equal diameter. If the total current entering the split is $$I_0$$, what is the current in each branch?

Accepted Answer

$$I_0/2$

Question 12

Which of the following is the correct SI unit for resistivity?

Accepted Answer

$$\Omega \cdot \mathrm{m}$$

Question 13

A carbon resistance thermometer has a resistance of $$0.030\ \Omega at an $$unknown temperature. If its resistance at $$20^{\circ}$$\mathrm{C}$$ is 0.028$$\ \Omega$$ and $$\alpha = -0.0005\ ^\circ\mathrm{C}^{-1}$$, what is the temperature?

Accepted Answer

$$122.9\ ^\circ\mathrm{C}$$

Question 14

Which of the following best explains why the conventional current is used instead of electron current in circuit analysis?

Accepted Answer

It is easier to measure the flow of charge than to count individual electrons.

Question 15

A wire has a non-uniform cross-sectional area $$A(x). $$What is the correct expression for its total resistance $$R$$ over length $$L$$?

Accepted Answer

$$R = \rho \$$int_0$$^L \dfrac{dx}{A(x)}$$

Question 16

If a wire's diameter is doubled while keeping its length and material the same, what happens to its resistance?

Accepted Answer

It becomes one-fourth as large.

Question 17

Which of the following is true about the relationship between current density $$\vec{J}$$ and electric field $$\vec{E} in a $$conductor that obeys Ohm's Law?

Accepted Answer

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

Question 18

A cylindrical shell of inner radius $$a$$ and outer radius $$b$$ has length $$L$$ and resistivity $$\rho. $$What is the resistance between the inner and outer surfaces?

Accepted Answer

$$R = \dfrac{\rho}{2\pi L} \ln \dfrac{b}{a}$$

Chapter 27: Current and Resistance – Structured Study Notes

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