Q: A $$5\ \mu\mathrm{F}$$ and a $$10\ \mu\mathrm{F}$$ capacitor are connected in parallel across a $$9\ \mathrm{V}$$ battery. What is the total energy stored in the capacitors?

$$6.08 \times 10$$^{-4}$$\ \mathrm{J}$$

Question 1

A parallel-plate capacitor is constructed using two plates of area $$A$$ separated by a distance $$d in $$vacuum. If a dielectric with dielectric constant $$\kappa is $$inserted fully between the plates, which of the following correctly describes the new capacitance $$C'$$ compared to the original capacitance $$C_0$$?

Accepted Answer

$$C' = \kappa C_0$

Question 2

Which of the following statements about capacitors in series is correct?

Accepted Answer

The total charge stored on each capacitor is the same.

Question 3

A cylindrical capacitor consists of two coaxial cylinders of length $$L$$, with inner radius $$r_a$$ and outer radius $$r_b$$ ($$r_b \u003e r_a). $$What is the capacitance per unit length of this system in vacuum?

Accepted Answer

$$\frac{2\pi \$$epsilon_0$$}{\ln(\frac{r_b}{r_a})}$$

Question 4

A $$10\ \mu\mathrm{F}$$ and a $$20\ \mu\mathrm{F}$$ capacitor are connected in series across a $$12\ \mathrm{V}$$ battery. What is the charge stored on the $$10\ \mu\mathrm{F}$$ capacitor?

Accepted Answer

$$80\ \mu\mathrm{C}$$

Question 5

Which of the following best describes the energy stored in a capacitor with charge $$Q$$ and voltage $$V$$?

Accepted Answer

$$U = \frac{1}{2} QV$$

Question 6

A resistor of $$100\ \Omega is $$connected to a $$10\ \mathrm{V}$$ battery. What is the current through the resistor?

Accepted Answer

$$0.1\ \mathrm{A}$$

Question 7

Which of the following is a correct statement of Ohm's Law for a uniform conductor?

Accepted Answer

$$V = IR$$

Question 8

A circuit contains three resistors: $$R_1 = 2$$\ \Omega$$, R_2$ = 3\ \Omega$$, and $$R_3 = 6$$\ \Omega$$ connected in parallel. What is the effective resistance of the network?

Accepted Answer

$$1\ \Omega$$

Question 9

In a simple RC circuit, a capacitor $$C is $$charged through a resistor $$R by a $$battery of emf $$\mathcal{E}. $$What is the expression for the charge $$q(t) on $$the capacitor at time $$t$$ after the switch is closed?

Accepted Answer

$$q(t) = C\mathcal{E}(1 - e$$^{-t/RC}$$)$$

Question 10

A $$12\ \mathrm{V}$$ battery is connected to a circuit with two resistors, $$R_1 = 4$$\ \Omega$$ and R_2$ = 8\ \Omega$$, in series. What is the voltage drop across $$R_2$$?

Accepted Answer

$$8\ \mathrm{V}$$

Question 11

Which of the following is true about the current in a series circuit containing only resistors?

Accepted Answer

The current is the same through all resistors.

Question 12

A $$5\ \mu\mathrm{F}$$ and a $$10\ \mu\mathrm{F}$$ capacitor are connected in parallel across a $$9\ \mathrm{V}$$ battery. What is the total energy stored in the capacitors?

Accepted Answer

$$6.08 	imes 10$$^{-4}$$\ \mathrm{J}$$

Question 13

Which of the following best describes the effect of inserting a dielectric material between the plates of a charged, isolated capacitor?

Accepted Answer

The voltage across the plates decreases.

Question 14

A wire of length $$L$$ and cross-sectional area $$A$$ has resistivity $$\rho. $$What is its resistance $$R$$?

Accepted Answer

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

Question 15

In a circuit, three resistors of $$2\ \Omega$$, $$3\ \Omega$$, and $$6\ \Omega$$ are connected in series. What is the total resistance?

Accepted Answer

$$11\ \Omega$$

Question 16

A $$100\ \Omega$$ resistor is connected in series with a $$200\ \Omega$$ resistor across a $$12\ \mathrm{V}$$ battery. What is the current in the circuit?

Accepted Answer

$$0.04\ \mathrm{A}$$

Question 17

Which of the following is a correct application of Kirchhoff's loop rule?

Accepted Answer

The sum of the potential differences around any closed loop is zero.

Question 18

A $$10\ \mu\mathrm{F}$$ capacitor is charged to $$5\ \mathrm{V}$$ and then disconnected from the battery. If a dielectric with $$\kappa = 2 is $$inserted, what happens to the energy stored in the capacitor?

Accepted Answer

It decreases by a factor of 2.

Question 19

In a discharging RC circuit, what is the expression for the current $$I(t) as a $$function of time?

Accepted Answer

$$I(t) = \frac{Q_0$}{RC} e$$^{-t/RC}$$

Physics 207: Circuits, Capacitance, and DC Circuits Study Notes

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