Q: A $$10\ \mathrm{V}$$ battery is connected to a series RC circuit with $$R = 2\ \mathrm{k}\Omega$$ and $$C = 5\ \mu\mathrm{F}. $$What is the charge on the capacitor after a long time?

$$5.0 \times 10$$^{-4}$$\ \mathrm{C}$$

Q: Which equation gives the charge $$Q(t) on a $$capacitor as it is charging in a series RC circuit?

$$Q(t) = Q_0$ (1 - e$$^{-t/\tau}$$)$$

Q: A $$10\ \mu\mathrm{F}$$ capacitor is charged to $$5\ \mathrm{V}$$ and then discharged through a $$1\ \mathrm{k}\Omega$$ resistor. How much energy is initially stored in the capacitor?

$$1.25 \times 10$$^{-4}$$\ \mathrm{J}$$

Question 1

A battery with an EMF of $$\varepsilon = 12\ \mathrm{V} is $$connected in series with two resistors, $$R_1 = 4$$\ \Omega$$ and R_2$ = 8\ \Omega. $$What is the current flowing through the circuit?

Accepted Answer

$$1.0\ \mathrm{A}$$

Question 2

Which of the following correctly describes the voltage drop across a resistor when moving in the direction of current flow?

Accepted Answer

The voltage drops by $$IR$$

Question 3

Three resistors, $$R_1 = 6$$\ \Omega$$, R_2$ = 3\ \Omega$$, and $$R_3 = 2$$\ \Omega$$, are connected in parallel. What is the equivalent resistance R$$_{eq}$$?

Accepted Answer

$$R_{eq} = 1.09\ \Omega$$

Question 4

A circuit contains a $$10\ \mathrm{V}$$ battery, a $$5\ \Omega$$ resistor, and a $$2\ \Omega$$ resistor in series. What is the power dissipated by the $$5\ \Omega$$ resistor?

Accepted Answer

$$5.1\ \mathrm{W}$$

Question 5

Which of the following statements about Kirchhoff's rules is correct?

Accepted Answer

The loop rule states that the sum of the voltage drops around a closed loop is zero.

Question 6

A $$100\ \mu\mathrm{F}$$ capacitor is charged to $$12\ \mathrm{V}$$ and then discharged through a $$1\ \mathrm{k}\Omega$$ resistor. What is the time constant $$	au$$ for this circuit?

Accepted Answer

$$0.12\ \mathrm{s}$$

Question 7

In a multi-loop circuit, you assign a current direction and later find a negative value for that current. What does this mean?

Accepted Answer

The current flows in the opposite direction to your initial assumption.

Question 8

A $$10\ \mathrm{V}$$ battery is connected to a series RC circuit with $$R = 2\ \mathrm{k}\Omega$$ and $$C = 5\ \mu\mathrm{F}. $$What is the charge on the capacitor after a long time?

Accepted Answer

$$5.0 	imes 10$$^{-4}$$\ \mathrm{C}$$

Question 9

Which equation gives the charge $$Q(t) on a $$capacitor as it is charging in a series RC circuit?

Accepted Answer

$$Q(t) = Q_0$ (1 - e$$^{-t/	au}$$)$$

Question 10

A $$9.0\ \mathrm{V}$$ battery is used to charge a $$100\ \mu\mathrm{F}$$ capacitor through a $$1.0\ \mathrm{k}\Omega$$ resistor. How long does it take for the capacitor to reach approximately $$63\% of $$its maximum charge?

Accepted Answer

$$0.1\ \mathrm{s}$$

Question 11

In a parallel circuit, which of the following is true?

Accepted Answer

The voltage drop across each resistor is the same.

Question 12

A $$10\ \mathrm{V}$$ battery is connected to a resistor of $$5\ \Omega$$ and a capacitor of $$2\ \mu\mathrm{F} in $$series. What is the initial current just after the switch is closed?

Accepted Answer

$$2\ \mathrm{A}$$

Question 13

Which of the following best describes the energy transformation in a discharging capacitor through a resistor?

Accepted Answer

Electrical energy is converted to thermal energy in the resistor.

Question 14

A $$20\ \Omega$$ and a $$30\ \Omega$$ resistor are connected in parallel. What is the equivalent resistance?

Accepted Answer

$$12\ \Omega$$

Question 15

If a capacitor in an RC circuit is initially uncharged, what is the voltage across the capacitor immediately after the switch is closed?

Accepted Answer

It is zero.

Question 16

A $$10\ \mu\mathrm{F}$$ capacitor is charged to $$5\ \mathrm{V}$$ and then discharged through a $$1\ \mathrm{k}\Omega$$ resistor. How much energy is initially stored in the capacitor?

Accepted Answer

$$1.25 	imes 10$$^{-4}$$\ \mathrm{J}$$

Question 17

In a circuit, the sum of the currents entering a junction is $$2\ \mathrm{A}$$, and the sum of the currents leaving is $$1.5\ \mathrm{A}. $$What does this indicate?

Accepted Answer

Charge is not conserved; there is a calculation error.

Question 18

A $$12\ \mathrm{V}$$ battery is connected to a series circuit with $$R = 6\ \Omega$$ and $$C = 100\ \mu\mathrm{F}. $$How long does it take for the voltage across the capacitor to reach $$9.48\ \mathrm{V}$$?

Accepted Answer

$$1.0\ \mathrm{s}$$

Question 19

Which of the following is the correct formula for the power dissipated by a resistor in a DC circuit?

Accepted Answer

All of the above

DC Circuits: EMF, Resistors, Kirchhoff's Rules, and RC Circuits

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