Q: Two spherical drops of mercury each have a charge of $$0.10\ \mathrm{nC}$$ and a potential of $$410\ \mathrm{V} at $$the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?

$$410 \times 2$$^{1/3}$$\ \mathrm{V}$$

Question 1

When two or more capacitors are connected in series across a potential difference, which of the following statements is true?

Accepted Answer

Each capacitor carries the same amount of charge.

Question 2

In the circuit shown, capacitors $$C_1$$ and $$C_2$$ are initially uncharged. The switch is first thrown to position A and kept there for a long time. It is then thrown to position B. Let the charges on the capacitors be $$Q_1$$, $$Q_2$$, and $$Q_3$$ and the potential differences across them be $$V_1$$, $$V_2$$, and $$V_3. $$Which of the following conditions must be true with the switch in position B?

Accepted Answer

$$V_1$$ + $$V_2$$ = $$V_3$$

Question 3

An ideal parallel-plate capacitor consists of a set of two parallel plates of area $$A$$ separated by a very small distance $$d. $$When this capacitor is connected to a battery that maintains a constant potential difference between the plates, the energy stored in the capacitor is $$U_0. If $$the separation between the plates is doubled, how much energy is stored in the capacitor?

Accepted Answer

$$U_0/2$

Question 4

A negative charge, if free, will tend to move:

Accepted Answer

From low potential to high potential.

Question 5

Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure. Which statement about the electric potential is true?

Accepted Answer

The potential at points A and B are equal, and the potential at point C is lower than the potential at point B.

Question 6

Two spherical drops of mercury each have a charge of $$0.10\ \mathrm{nC}$$ and a potential of $$410\ \mathrm{V} at $$the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?

Accepted Answer

$$410 	imes 2$$^{1/3}$$\ \mathrm{V}$$

Question 7

A circuit consists of a $$9\ \mathrm{V}$$ battery, a $$4\ \Omega$$ resistor, and a $$3\ \mathrm{V}$$ battery connected in series as shown. What is the current through the resistor?

Accepted Answer

$$1.5\ \mathrm{A}$$, from left to right

Question 8

In the circuit shown, how much current flows through the $$12\ \Omega$$ resistor, and in what direction (up or down the page)?

Accepted Answer

$$0.25\ \mathrm{A}$$, down the page

Question 9

A copper wire has a diameter of $$0.8\ \mathrm{mm}. $$What is the current in the wire if the resistivity of copper is $$1.7 	imes 10$$^{-8}$$\ \Omega\mathrm{m}$$ and the potential difference across a $$2\ \mathrm{m}$$ length of wire is $$1.0\ \mathrm{V}$$?

Accepted Answer

$$2.5\ \mathrm{A}$$

Question 10

In the circuit shown, find the current $$I_1$$ through the $$3.0\ \Omega$$ resistor.

Accepted Answer

$$1.0\ \mathrm{A}$$

Question 11

In the circuit shown, find the emf $$\varepsilon of $$the battery on the right if the current through the $$2.0\ \Omega$$ resistor is $$1.0\ \mathrm{A}.$$

Accepted Answer

$$6.0\ \mathrm{V}$$

Question 12

A battery of $$30\ \mathrm{V} is $$connected to a circuit with capacitors $$C_1 = 15$$\ \mu\mathrm{F}$$, C_2$ = 30\ \mu\mathrm{F}$$, and $$C_3 = 30$$\ \mu\mathrm{F}$$ as shown. The switch is flipped to position B. What is the charge on capacitor C_1$?

Accepted Answer

$$300\ \mu\mathrm{C}$$

Question 13

In the same circuit, what is the potential difference across capacitor $$C_2$$ after the switch is flipped to position B?

Accepted Answer

$$30\ \mathrm{V}$$

Question 14

A $$9\ \mathrm{V}$$ battery is connected in series with a $$4\ \Omega$$ resistor and a $$3\ \mathrm{V}$$ battery (opposing polarity). What is the power dissipated in the resistor?

Accepted Answer

$$4.5\ \mathrm{W}$$

Question 15

In the triangle circuit with $$9\ \mathrm{V}$$ and $$15\ \mathrm{V}$$ batteries and $$12\ \Omega$$ and $$24\ \Omega$$ resistors, what is the direction of current through the bottom wire?

Accepted Answer

From right to left

Question 16

A wire of length $$2\ \mathrm{m}$$ and diameter $$0.8\ \mathrm{mm}$$ carries a current of $$2.5\ \mathrm{A}. $$What is the electric field inside the wire if the resistivity of copper is $$1.7 	imes 10$$^{-8}$$\ \Omega\mathrm{m}$$?

Accepted Answer

$$0.0217\ \mathrm{V/m}$$

Question 17

A parallel-plate capacitor is connected to a battery and then disconnected. If the plate separation is doubled, what happens to the potential difference across the plates?

Accepted Answer

It doubles.

Question 18

Which of the following best describes the energy stored in a capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$

Capacitors, Electric Potential, and DC Circuits: Study Notes and Practice Problems

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