Q: A $$2.0\,\text{cm}$$ diameter parallel-plate capacitor with $$0.50\,\text{mm}$$ spacing is charged to $$200\,\text{V}. $$What is the total energy stored in the electric field?

$$U \approx 1.1 \times 10$$^{-7}$$\,\text{J}$$

Q: In an ionic solution, $$5.0 \times 10$$^{15}$$ positive ions with charge +2e$ move to the right each second, while 6.0$$ \times $$10^{15}$$ negative ions with charge $$-e$$ move to the left. What is the magnitude and direction of the net current?

$$2.6\,\text{mA} to $$the right

Q: A rear window defroster wire is $$12.2\,\text{m}$$ long, $$1.8\,\text{mm}$$ wide, and $$0.11\,\text{mm}$$ thick. Connected to a $$12.0\,\text{V}$$ battery, it draws $$7.5\,\text{A}. $$What is the resistivity of the wire material?

$$2.6 \times 10$$^{-8}$$\,\Omega \cdot \text{m}$$

Q: Two lightbulbs, $$100\,\text{W}$$ and $$60\,\text{W}$$, are operated at the same current ($$0.5\,\text{A}). $$Which is brighter?

The $$60\,\text{W}$$ bulb is brighter.

Question 1

A parallel-plate capacitor is charged to a potential difference $$\Delta V_C$$ and then disconnected from all wires and batteries. If the plate separation is doubled from $$d to$$ $$2d$$, which of the following statements is correct regarding the charge $$Q on $$the plates?

Accepted Answer

The charge $$Q$$ remains constant.

Question 2

For the same scenario as above, what happens to the electric field strength $$E$$ between the plates when the separation is doubled?

Accepted Answer

The electric field strength $$E$$ remains constant.

Question 3

A parallel-plate capacitor with plate area $$A$$ and separation $$d is $$filled with a dielectric of constant $$\kappa. $$Which equation correctly gives its capacitance $$C$$?

Accepted Answer

$$C = \kappa \$$varepsilon_0$$ \frac{A}{d}$$

Question 4

A homemade capacitor uses two $$35\,	ext{cm} 	imes 35\,	ext{cm}$$ sheets of aluminum foil separated by a $$0.25\,	ext{mm}$$ thick sheet of paper ($$\kappa = 3.0). $$What is the capacitance?

Accepted Answer

$$C \approx 13\,	ext{nF}$$

Question 5

A $$2.0\,	ext{cm} 	imes 2.0\,	ext{cm} 	imes 2.0\,	ext{cm}$$ region contains $$50\,	ext{pJ} of $$energy stored in a uniform electric field. What is the electric field strength $$E$$?

Accepted Answer

$$E \approx 1200\,	ext{V/m}$$

Question 6

A $$2.0\,	ext{cm}$$ diameter parallel-plate capacitor with $$0.50\,	ext{mm}$$ spacing is charged to $$200\,	ext{V}. $$What is the total energy stored in the electric field?

Accepted Answer

$$U \approx 1.1 	imes 10$$^{-7}$$\,	ext{J}$$

Question 7

In an ionic solution, $$5.0 	imes 10$$^{15}$$ positive ions with charge +2e$ move to the right each second, while 6.0$$ 	imes $$10^{15}$$ negative ions with charge $$-e$$ move to the left. What is the magnitude and direction of the net current?

Accepted Answer

$$2.6\,	ext{mA} to $$the right

Question 8

Refer to the wire junction diagram. If $$5\,	ext{A}$$ enters the junction and splits into $$3\,	ext{A}$$ and two unknown branches, with $$1\,	ext{A} in $$branch B, what is the current in branch C?

Accepted Answer

$$2\,	ext{A} to $$the right

Question 9

A $$9.0\,	ext{V}$$ battery supplies a $$2.5\,	ext{mA}$$ current to a circuit for $$5.0\,	ext{h}. $$How much charge is transferred?

Accepted Answer

$$45\,	ext{C}$$

Question 10

Which of the following statements about batteries is FALSE?

Accepted Answer

A battery is a source of constant current.

Question 11

The resistance $$R of a $$wire is given by $$R = \rho \frac{L}{A}$$, where $$\rho is $$resistivity, $$L is $$length, and $$A is $$cross-sectional area. If two wires have the same material but one is twice as long and half the radius, how does its resistance compare to the other?

Accepted Answer

Its resistance is eight times greater.

Question 12

A rear window defroster wire is $$12.2\,	ext{m}$$ long, $$1.8\,	ext{mm}$$ wide, and $$0.11\,	ext{mm}$$ thick. Connected to a $$12.0\,	ext{V}$$ battery, it draws $$7.5\,	ext{A}. $$What is the resistivity of the wire material?

Accepted Answer

$$2.6 	imes 10$$^{-8}$$\,\Omega \cdot 	ext{m}$$

Question 13

Two lightbulbs, $$100\,	ext{W}$$ and $$60\,	ext{W}$$, are operated at the same current ($$0.5\,	ext{A}). $$Which is brighter?

Accepted Answer

The $$60\,	ext{W}$$ bulb is brighter.

Question 14

An electric eel develops a potential difference of $$450\,	ext{V}$$, driving a current of $$0.80\,	ext{A}$$ for a $$1.0\,	ext{ms}$$ pulse. What is the total energy delivered in this pulse?

Accepted Answer

$$0.36\,	ext{J}$$

Question 15

Which equation correctly relates the energy density $$u_E of an $$electric field to the field strength $$E$$ and permittivity $$\$$varepsilon_0$$?

Accepted Answer

$$u_E = \frac{1}{2} \$$varepsilon_0$$ E^2$

Question 16

A battery supplies a constant voltage $$V to a $$circuit. If the circuit resistance $$R is $$doubled, what happens to the current $$I$$?

Accepted Answer

The current $$I is $$halved.

Question 17

A parallel-plate capacitor is charged and then disconnected. If the plate separation is tripled, what happens to the potential difference $$\Delta V_C$$?

Accepted Answer

The potential difference $$\Delta V_C$$ triples.

Applying Conservation of Charge to Junctions in a Circuit

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