Q: A circuit contains a $$6\ \mathrm{V}$$ battery and two resistors, $$1\ \Omega$$ and $$2\ \Omega$$, in series. What is the voltage drop across the $$2\ \Omega$$ resistor?

$$V = (2\ \Omega) \times 2.0\ \mathrm{A} = 4.0\ \mathrm{V}$$

Question 1

In the circuit shown in the first image, bulbs A, B, and C are identical. Rank the bulbs from brightest to dimmest. Which equation best explains your reasoning?

Accepted Answer

A is brightest, B and C are equally bright but dimmer than A. $$P = I^2$ R$$ explains the ranking.

Question 2

If a wire is connected between points 1 and 2 in the first image, what happens to each bulb?

Accepted Answer

Bulb A gets brighter, bulbs B and C go out.

Question 3

For the circuit in the second image, what is the total current flowing through the circuit?

Accepted Answer

$$I = \frac{6\ \mathrm{V}}{1\ \Omega + 2\ \Omega} = 2.0\ \mathrm{A}$$

Question 4

In the third image, what is the equivalent resistance between points a and b?

Accepted Answer

$$R_{eq} = 24\ \Omega$$

Question 5

Which combination of three $$1.0\ \mathrm{k}\Omega$$ resistors gives the smallest possible equivalent resistance?

Accepted Answer

All three resistors in parallel: $$R_{eq} = 0.33\ \mathrm{k}\Omega$$

Question 6

In the circuit shown in the fifth image, the ammeter reads $$3.0\ \mathrm{A}. $$What is the value of $$I_1$$?

Accepted Answer

$$I_1 = 1.0$$\ \mathrm{A}$$

Question 7

In the same circuit (fifth image), what is the emf $$\varepsilon of $$the right battery?

Accepted Answer

$$\varepsilon = 15.0\ \mathrm{V}$$

Question 8

For the circuit in the last image, what is the total current supplied by the battery?

Accepted Answer

$$I_{total} = 0.50\ \mathrm{A}$$

Question 9

In the last image, what is the potential difference across the $$12\ \Omega$$ resistor?

Accepted Answer

$$\Delta V = 6.0\ \mathrm{V}$$

Question 10

In the last image, what is the current through the $$30\ \Omega$$ resistor?

Accepted Answer

$$I = 0.20\ \mathrm{A}$$

Question 11

Which of the following statements about combining resistors is correct?

Accepted Answer

The equivalent resistance of resistors in parallel is always less than the smallest individual resistance.

Question 12

A $$12\ \mathrm{V}$$ battery is connected to a circuit with a $$12\ \Omega$$ resistor in series with a parallel combination of $$20\ \Omega$$ and $$30\ \Omega$$ resistors. What is the equivalent resistance of the parallel section?

Accepted Answer

$$R_{parallel} = 12\ \Omega$$

Question 13

If the resistance of each bulb in the first image is doubled, what happens to the brightness of bulb A?

Accepted Answer

It decreases because the total resistance increases, reducing the current.

Question 14

In the circuit with three $$1.0\ \mathrm{k}\Omega$$ resistors, which configuration gives an equivalent resistance of $$1.5\ \mathrm{k}\Omega$$?

Accepted Answer

Two resistors in parallel, then in series with the third.

Question 15

A circuit contains a $$6\ \mathrm{V}$$ battery and two resistors, $$1\ \Omega$$ and $$2\ \Omega$$, in series. What is the voltage drop across the $$2\ \Omega$$ resistor?

Accepted Answer

$$V = (2\ \Omega) 	imes 2.0\ \mathrm{A} = 4.0\ \mathrm{V}$$

Step-by-Step Guidance for Circuits and Resistance Problems (Chapter 23)

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