Q: A $$10\ \mu F$$ capacitor initially charged to $$20\ \mu C is $$discharged through a $$1\ k\Omega$$ resistor. How long does it take for the charge to drop to $$10\ \mu C$$?

$$t = \tau \ln 2 = (1\ k\Omega \times 10\ \mu F) \ln 2 = 0.01\ s \times 0.693 = 6.93\ ms$$

Question 1

Which of the following correctly describes Kirchhoff’s Current Junction Law?

Accepted Answer

The current entering a junction is equal to the current leaving the junction: $$I_{in} = I_{out}.$$

Question 2

A circuit consists of a 15 V battery and a 5 $$\Omega$$ resistor in series. What is the current through the resistor?

Accepted Answer

$$I = \frac{15\ V}{5\ \Omega} = 3\ A$$

Question 3

Which equation correctly expresses Ohm’s Law?

Accepted Answer

$$\Delta V = IR$$

Question 4

In a series circuit with resistors $$R_1 = 10$$\ \Omega$$ and R_2$ = 5\ \Omega$$ connected to a $$30\ V$$ battery, what is the equivalent resistance?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ = 15\ \Omega$$

Question 5

A parallel circuit has $$R_1 = 10$$\ \Omega$$ and R_2$ = 5\ \Omega. $$What is the equivalent resistance?

Accepted Answer

$$R_{eq} = \frac{1}{\frac{1}{10} + \frac{1}{5}} = 3.33\ \Omega$$

Question 6

A 9 V battery is connected to two resistors in parallel: $$9\ \Omega$$ and $$1\ \Omega. $$What is the total current supplied by the battery?

Accepted Answer

$$I_{total} = \frac{9\ V}{0.9\ \Omega} = 10\ A$$

Question 7

Which statement about grounding a circuit is correct?

Accepted Answer

Grounding a circuit sets the potential at the ground point to zero volts.

Question 8

A $$10\ \mu F$$ capacitor initially charged to $$20\ \mu C is $$discharged through a $$1\ k\Omega$$ resistor. How long does it take for the charge to drop to $$10\ \mu C$$?

Accepted Answer

$$t = 	au \ln 2 = (1\ k\Omega 	imes 10\ \mu F) \ln 2 = 0.01\ s 	imes 0.693 = 6.93\ ms$$

Question 9

Which formula gives the charge on a discharging capacitor at time $$t$$?

Accepted Answer

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

Question 10

A real battery has an internal resistance $$r. If a $$battery with emf $$\epsilon$$ and internal resistance $$r is $$connected to a resistor $$R$$, what is the terminal voltage?

Accepted Answer

$$V_{terminal} = \epsilon - Ir$$

Question 11

A $$24\ V$$ battery is connected to three resistors in parallel: $$3\ \Omega$$, $$3\ \Omega$$, and $$5\ \Omega. $$What is the equivalent resistance?

Accepted Answer

$$R_{eq} = \frac{1}{\frac{1}{3} + \frac{1}{3} + \frac{1}{5}} = 1.07\ \Omega$$

Question 12

Which device should be connected in parallel to measure voltage across a resistor?

Accepted Answer

Voltmeter

Question 13

A $$9\ V$$ battery is rated at $$450\ mA\cdot hr. $$How long will it last if a device draws $$225\ mA$$?

Accepted Answer

2 hours

Question 14

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

Accepted Answer

The current is the same through all resistors.

Question 15

A $$6\ V$$ battery is connected to a $$100\ \Omega$$ resistor and a $$300\ \Omega$$ resistor in series. What is the current in the circuit?

Accepted Answer

$$I = \frac{6\ V}{100\ \Omega + 300\ \Omega} = 0.015\ A$$

Question 16

A $$4\ \mu F$$ capacitor is charged to $$9\ V$$ and then discharged through a $$25\ \Omega$$ resistor. What is the initial current just after the switch is closed?

Accepted Answer

$$I_0$$ = \frac{9\ V}{25\ \Omega} = 0.36\ A$$

Question 17

Which of the following best describes the time constant $$	au in an RC $$circuit?

Accepted Answer

$$	au = RC$$, the time for the charge or voltage to decrease to $$\frac{1}{e} of $$its initial value.

Question 18

A light bulb is rated at $$5.4\ W$$ and operates at $$3.0\ V. $$What is the current through the bulb?

Accepted Answer

$$I = \frac{P}{V} = \frac{5.4\ W}{3.0\ V} = 1.8\ A$$

Question 19

If a battery with emf $$\epsilon = 12\ V$$ and internal resistance $$r = 0.2\ \Omega is $$short-circuited, what is the maximum current?

Accepted Answer

$$I_{max} = \frac{12\ V}{0.2\ \Omega} = 60\ A$$

Fundamentals of Circuits: Series, Parallel, and RC Circuits

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