Q: A $$9.0\ \mathrm{V}$$ battery with internal resistance $$0.50\ \Omega is $$connected to a $$6.0\ \Omega$$ resistor. What is the terminal voltage of the battery when current is flowing?

$$V_{terminal} = 9.0 - I \times 0.50$$

Question 1

A battery with emf $$\varepsilon$$ and internal resistance $$r is $$connected to an external resistor $$R. $$Which equation correctly gives the terminal voltage $$V_{ab}$$ across the battery terminals?

Accepted Answer

$$V_{ab} = \varepsilon - Ir$$

Question 2

In the circuit shown, $$R = 65.0\ \Omega$$, $$r = 0.5\ \Omega$$, and $$\varepsilon = 12.0\ \mathrm{V}. $$What is the current $$I in $$the circuit?

Accepted Answer

$$I = \dfrac{12.0}{65.0 + 0.5}\ \mathrm{A}$$

Question 3

Which of the following is true for resistors in series?

Accepted Answer

The total resistance is the sum of the individual resistances: $$R_{eq} = R_1$ + R_2$ + R_3$ + \ldots$$

Question 4

In a parallel circuit with three resistors $$R_1$$, $$R_2$$, and $$R_3$$, which statement is correct?

Accepted Answer

The voltage across each resistor is the same.

Question 5

Three identical lightbulbs are connected in parallel to a battery. If one bulb burns out, what happens to the brightness of the remaining bulbs?

Accepted Answer

The brightness of the remaining bulbs stays the same.

Question 6

Which configuration produces more light: two identical bulbs in series or in parallel (assuming the same battery is used)?

Accepted Answer

Parallel, because each bulb receives the full battery voltage.

Question 7

A circuit contains a $$400\ \Omega$$ resistor in series with a $$1000\ \Omega$$ resistor, both in parallel with a $$500\ \Omega$$ resistor, all connected to a $$12\ \mathrm{V}$$ battery. What is the first step to find the total current drawn from the battery?

Accepted Answer

Find the equivalent resistance of the $$400\ \Omega$$ and $$1000\ \Omega$$ resistors in series, then combine with the $$500\ \Omega in $$parallel.

Question 8

A $$9.0\ \mathrm{V}$$ battery with internal resistance $$0.50\ \Omega is $$connected to a $$6.0\ \Omega$$ resistor. What is the terminal voltage of the battery when current is flowing?

Accepted Answer

$$V_{terminal} = 9.0 - I 	imes 0.50$$

Question 9

Which of the following is Kirchhoff’s junction rule?

Accepted Answer

The sum of the currents entering a junction equals the sum of the currents leaving it.

Question 10

In a circuit with two batteries in series, one with $$\$$varepsilon_1$$ = 20\ \mathrm{V}$$ and the other with $$\$$varepsilon_2$$ = 12\ \mathrm{V}$$, both oriented in the same direction, what is the total emf?

Accepted Answer

$$\varepsilon_{total} = 32\ \mathrm{V}$$

Question 11

A circuit contains a resistor $$R$$ and a capacitor $$C in $$series with a battery of emf $$\varepsilon. $$The switch is closed at $$t=0. $$Which equation describes the charge $$Q on $$the capacitor as a function of time?

Accepted Answer

$$Q(t) = C\varepsilon (1 - e$$^{-t/RC}$$)$$

Question 12

In a steady-state DC circuit, what is the current through a fully charged capacitor?

Accepted Answer

It is zero.

Question 13

Which of the following best describes the voltage change across a resistor when traversing in the direction of current flow, according to Kirchhoff’s loop rule?

Accepted Answer

Voltage decreases.

Question 14

A $$1.0\ \mu\mathrm{F}$$ capacitor is charged through a $$1.0\ \mathrm{M}\Omega$$ resistor by a $$10\ \mathrm{V}$$ battery. What is the time constant $$	au of $$the circuit?

Accepted Answer

$$	au = 1.0\ \mathrm{M}\Omega 	imes 1.0\ \mu\mathrm{F} = 1.0\ \mathrm{s}$$

Question 15

A real-world application: In a car, the headlights are wired in parallel. What is the main advantage of this configuration?

Accepted Answer

If one headlight fails, the other remains on.

Question 16

A circuit contains a $$12\ \mathrm{V}$$ battery, a $$400\ \Omega$$ resistor, and a $$290\ \Omega$$ resistor in series. What is the voltage drop across the $$400\ \Omega$$ resistor?

Accepted Answer

$$V = 12 	imes \dfrac{400}{400 + 290}$$

Question 17

Which of the following is NOT a correct step in applying Kirchhoff’s rules to a circuit?

Accepted Answer

Assume all currents are equal in every branch.

Question 18

In an RC circuit, which graph best represents the current $$I as a $$function of time during the charging process?

Accepted Answer

A graph that starts at a maximum and decays exponentially to zero.

DC Circuits: Series, Parallel, and RC Circuits

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