Q: A potassium ion channel opens for $$1\ \mathrm{ms}$$ and passes $$1.1 \times 10^4$ potassium ions. Each ion has charge e = 1.6$$ \times $$10^{-19}$$\ \mathrm{C}$$. What is the total charge that passes through the channel?

$$1.8 \times 10$$^{-15}$$\ \mathrm{C}$$

Q: A current of $$1.8\ \mathrm{pA}$$ flows through an ion channel with a cross-sectional area of $$7.07 \times 10$$^{-20}$$\ \mathrm{m}^2. $$What is the current density $$J$$?

$$2.5 \times 10^7$\ \mathrm{A/m}^2$$

Question 1

A copper wire of length $$L$$ and cross-sectional area $$A$$ has a resistivity $$\rho. $$What is the correct formula for its resistance $$R$$?

Accepted Answer

$$R = \rho L / A$$

Question 2

Which of the following correctly describes the direction of conventional current in a wire?

Accepted Answer

It is in the direction of positive charge flow.

Question 3

A potassium ion channel opens for $$1\ \mathrm{ms}$$ and passes $$1.1 	imes 10^4$ potassium ions. Each ion has charge e = 1.6$$ 	imes $$10^{-19}$$\ \mathrm{C}$$. What is the total charge that passes through the channel?

Accepted Answer

$$1.8 	imes 10$$^{-15}$$\ \mathrm{C}$$

Question 4

Given a current $$I$$ passing through a resistor $$R$$ with voltage $$V$$ across it, which equation correctly relates power $$P$$ dissipated in the resistor?

Accepted Answer

$$P = IV$$

Question 5

A wire has twice the length and half the cross-sectional area of another wire, both made of the same material. How does its resistance compare?

Accepted Answer

It is four times greater.

Question 6

Which of the following is the correct expression for current density $$\vec{J} in $$terms of charge carrier density $$n$$, charge $$q$$, and drift velocity $$\vec{v}_d$$?

Accepted Answer

$$\vec{J} = nq\vec{v}_d$$

Question 7

If the voltage across a resistor is doubled, what happens to the power dissipated, assuming resistance remains constant?

Accepted Answer

Power increases by a factor of 4.

Question 8

Which of the following best describes Ohm's law at the microscopic level?

Accepted Answer

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

Question 9

A metal conductor contains many free electrons moving randomly. When an electric field is applied, what happens?

Accepted Answer

Electrons acquire a small drift velocity superposed on their random motion.

Question 10

Which of the following is the correct formula for the current $$I$$ through a surface when the current density $$\vec{J} is $$not perpendicular to the surface?

Accepted Answer

$$I = \vec{J} \cdot \vec{A}$$

Question 11

A resistor is connected to a $$2\ \mathrm{V}$$ battery. If the resistance is halved, what happens to the current through the resistor?

Accepted Answer

It doubles.

Question 12

Which of the following statements about resistivity $$\rho is $$correct?

Accepted Answer

It is a property of the material and does not depend on the shape or size.

Question 13

A current of $$1.8\ \mathrm{pA}$$ flows through an ion channel with a cross-sectional area of $$7.07 	imes 10$$^{-20}$$\ \mathrm{m}^2. $$What is the current density $$J$$?

Accepted Answer

$$2.5 	imes 10^7$\ \mathrm{A/m}^2$$

Question 14

Which of the following is true for the direction of current $$I$$ when negative charges move to the right?

Accepted Answer

Current is to the left.

Question 15

Which of the following is the correct formula for instantaneous current?

Accepted Answer

$$I = \frac{dQ}{dt}$$

Question 16

If a material has a conductivity $$\sigma$$, what is its resistivity $$\rho$$?

Accepted Answer

$$\rho = 1/\sigma$$

Question 17

Which of the following is a correct statement about Ohm's law?

Accepted Answer

It is an empirical law that holds approximately for many materials.

Question 18

A battery supplies a current of $$20\ \mathrm{mA}$$ through the human body. Which of the following is a possible consequence?

Accepted Answer

Fibrillation of the heart; death within minutes.

Question 19

Which equation correctly relates the current $$I to $$the number density of charge carriers $$n$$, charge $$q$$, cross-sectional area $$A$$, and drift velocity $$v_d$$?

Accepted Answer

$$I = nAqv_d$$

Question 20

Which of the following is the correct formula for power dissipated in a resistor in terms of voltage $$V$$ and resistance $$R$$?

Accepted Answer

$$P = \frac{V^2$}{R}$$

Electric Current, Resistance, and Power: Study Notes

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