Question 1

A parallel-plate capacitor with plates separated by $$d is $$fully charged by a battery and then disconnected. The plates are then pulled apart until they are separated by $$2d. $$What is the ratio of the final to initial electrostatic energies, $$U_f/U_i$$?

Accepted Answer

$$2$$

Question 2

A camera flash uses a capacitor to release a large amount of energy in a short time. Which property of capacitors makes them suitable for this application?

Accepted Answer

They can store energy and release it quickly when needed.

Question 3

When a dielectric is inserted between the plates of a capacitor that has been disconnected from the battery, what happens to the potential difference $$\Delta V_C$$ between the plates?

Accepted Answer

$$\Delta V_C$$ decreases

Question 4

A parallel-plate capacitor is fully charged by a battery, and the battery remains connected. A dielectric is inserted between the plates. What happens to the charge $$q on $$the plates?

Accepted Answer

$$q$$ increases

Question 5

A parallel plate capacitor is made with a separation between plates of $$6.3 	imes 10$$^{-7}$$ m, and the gap is filled with a dielectric with $$\kappa = 9.6$$. To make a capacitor with a capacitance of 1.5$$ 	imes $$10^{-3} F$$, what area plates do you need? ($$\$$epsilon_0$$ = 8.85 	imes 10$$^{-12}$$ F/m)

Accepted Answer

$$1 m$^2$$

Question 6

A stud finder uses a capacitor with its plates arranged side by side. When the device is moved over a stud, what happens to the capacitance and why?

Accepted Answer

Capacitance increases because the stud acts as a dielectric material.

Question 7

In metals, the electron current is given by $$I_e = n_e A v_d$$, where $$n_e is $$the electron density, $$A is $$the cross-sectional area, and $$v_d is $$the drift speed. If the drift speed doubles, what happens to the electron current?

Accepted Answer

It doubles

Question 8

Consider two cylindrical segments of wire made of the same material and connected end to end. Segment 1 has half the radius of segment 2, and both segments have the same length. How do the currents $$I_1$$ and $$I_2$$, and current densities $$J_1$$ and $$J_2$$ compare?

Accepted Answer

$$I_1$$ = $$I_2$$, $$J_1 = 4J_2$

Question 9

The conductivity $$\sigma of a $$wire is given by $$\sigma = \frac{n_e e^2$ 	au}{m_e}$$, where $$	au is $$the mean time between collisions. Why does copper have a higher conductivity than nichrome?

Accepted Answer

The electrons' mean time between collisions in copper is higher than in nichrome.

Question 10

In an ohmic material, the current $$I is $$related to the potential difference $$\Delta V$$ and resistance $$R by$$ $$I = \frac{\Delta V}{R}. If $$you halve the potential difference across the wire, what happens to the current?

Accepted Answer

The current halves

Question 11

For a given potential difference across a length of wire, which of the following changes will increase the current by a factor of 4? (Select all that apply)

Accepted Answer

Use a material with a resistivity a quarter that of the original wire

Question 12

Household wiring typically uses copper, while toasters use nichrome wire. What is the main reason for this difference?

Accepted Answer

Copper has higher conductivity, resulting in less energy loss as heat.

Question 13

Superconducting materials reach a state where below a certain temperature, there is no resistance to current. What is a consequence of this phenomenon?

Accepted Answer

Magnetic fields do not penetrate the material, leading to the Meissner effect.

Question 14

A vertical wire carries current upward through the center of a horizontal table. A compass rests on the table. Which direction does the north pole of the compass point?

Accepted Answer

Tangential to the circle, following the right-hand rule

Question 15

When a magnet is broken in half, what happens to its magnetic poles?

Accepted Answer

Each piece forms a new north and south pole.

Question 16

Which of the following best describes the direction of current in metals?

Accepted Answer

It is the direction positive charge would move, opposite to electron flow.

Question 17

The resistance $$R of an $$ohmic conductor is given by $$R = \frac{\rho L}{A}$$, where $$\rho is $$resistivity, $$L is $$length, and $$A is $$cross-sectional area. If you double the length and halve the area, what happens to the resistance?

Accepted Answer

It increases by a factor of 4

Question 18

The net magnetic field from multiple sources is found by:

Accepted Answer

Adding the vector sum of the magnetic fields from each source: $$\vec{B}_{	ext{total}} = \vec{B}_1 + \vec{B}_2 + \ldots$$

Question 19

A long straight wire with a current produces a magnetic field. If you point your right hand thumb in the direction of current, your fingers curl in the direction of:

Accepted Answer

The magnetic field produced by the current

Capacitors, Current, Resistance, and Magnetic Fields: Study Notes 27

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