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 $r_b$ ($r_b > r_a$). 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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