Question 1

A parallel-plate capacitor is constructed using two plates of area $$A$$ separated by a distance $$d$$ and filled with a dielectric of constant $$\kappa. $$Which equation correctly gives the capacitance $$C of $$this capacitor?

Accepted Answer

$$C = \kappa \$$epsilon_0$$ \dfrac{A}{d}$$

Question 2

A cell membrane can be modeled as a parallel-plate capacitor. If the membrane thickness $$d is $$halved while the area $$A$$ and dielectric constant $$\kappa$$ remain unchanged, what happens to the capacitance?

Accepted Answer

It is doubled.

Question 3

A capacitor is charged to a potential difference $$\Delta V_C$$ and then disconnected from the battery. If the plates are pulled farther apart, which of the following statements is correct?

Accepted Answer

$$Q$$ stays constant, $$\Delta V_C$$ increases

Question 4

The energy stored in a capacitor is given by $$U_C = \dfrac{1}{2} C \Delta V_C^2$. If a camera flash capacitor stores 10$$\ \mathrm{mJ}$$ at 300$$\ \mathrm{mV}$$, what potential difference is required to store 90$$\ \mathrm{mJ}$$?

Accepted Answer

$$900\ \mathrm{mV}$$

Question 5

A capacitor is connected to a battery and then a dielectric is inserted between the plates while the battery remains connected. What happens to the charge $$Q$$ and the potential difference $$\Delta V_C$$?

Accepted Answer

$$Q$$ increases, $$\Delta V_C$$ stays constant

Question 6

The energy density $$u_E of $$the electric field in a parallel-plate capacitor is given by which of the following equations?

Accepted Answer

$$u_E = \dfrac{1}{2} \$$epsilon_0$$ E^2$

Question 7

The Nernst potential across a cell membrane is given by $$\Delta V = \dfrac{k_B T}{e} \ln \dfrac{c_{out}}{c_{in}}. If$$ $$c_{out} \u003e c_{in}$$, what is the sign of $$\Delta V$$?

Accepted Answer

It is positive.

Question 8

Which of the following best describes the function of the sodium-potassium pump in a cell membrane?

Accepted Answer

It uses ATP to move Na$$^+$$ out and K$$^+ in$$, creating a charge separation.

Question 9

A wire carries a current of $$I = 2\ \mathrm{A}. $$How much charge passes through a cross-section of the wire in $$5\ \mathrm{s}$$?

Accepted Answer

$$10\ \mathrm{C}$$

Question 10

A copper wire has a diameter of $$1.628 	imes 10$$^{-3}$$\ \mathrm{m}$$ and a resistivity $$ho_{copper} = 1.7 	imes 10$$^{-8}$$\ \Omega \cdot \mathrm{m}. $$What length $$L$$ would give a resistance of $$150\ \Omega$$?

Accepted Answer

$$73.5\ \mathrm{km}$$

Question 11

Which of the following is true for an ideal wire in a circuit?

Accepted Answer

All points in the wire are at the same potential.

Question 12

Ohm’s law relates the current $$I$$ through a resistor to the potential difference $$\Delta V_R$$ and resistance $$R. $$Which equation expresses Ohm’s law?

Accepted Answer

$$I = \dfrac{\Delta V_R}{R}$$

Question 13

A resistor is connected to a battery. If the resistance is doubled while the battery voltage remains the same, what happens to the current?

Accepted Answer

It is halved.

Question 14

Which of the following statements about electric current is correct?

Accepted Answer

Current is defined as the rate at which charge flows through a cross-section.

Question 15

A lightbulb is connected in a circuit with a battery and wires. In which situation will the bulb light up?

Accepted Answer

When there is a closed loop allowing current to flow from the battery, through the bulb, and back to the battery.

Question 16

The resistance $$R of a $$wire of length $$L$$ and cross-sectional area $$A$$ made of material with resistivity $$\rho is $$given by:

Accepted Answer

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

Question 17

A battery supplies a current $$I at a $$potential difference $$\Delta V_{bat}. $$What is the power delivered by the battery?

Accepted Answer

$$P_{bat} = I \Delta V_{bat}$$

Question 18

Which of the following best explains why the energy stored in a capacitor is proportional to the square of the voltage?

Accepted Answer

Because the work required to move each additional charge increases linearly with the amount of charge already on the plates.

Capacitance, Current, and Resistance: Foundations and Applications

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