Q: A circuit consists of a 9 V battery, a $$2\ \Omega$$ internal resistance, and a $$10\ \Omega$$ external resistor. What is the terminal voltage of the battery when the circuit is closed?

$$V_{\text{terminal}} = 7.5\ \text{V}$$

Q: If a battery's emf is $$V_0$$ and its internal resistance is $$r$$, what is the maximum current the battery can supply?

$$I_{\text{max}} = \frac{V_0$}{r}$$

Q: Which of the following is the correct expression for the total resistance $$R_{\text{eq}} of $$two resistors $$R_1$$ and $$R_2 in $$parallel?

$$R_{\text{eq}} = \frac{R_1$ R_2$}{R_1$ + R_2$}$$

Question 1

A battery with an emf $$V_0$$ and internal resistance $$r is $$connected to a resistor $$R. $$What is the current $$I in $$the circuit?

Accepted Answer

$$I = \frac{V_0$}{R + r}$$

Question 2

Which of the following best describes the function of the internal resistance $$r in a $$real battery?

Accepted Answer

It causes the terminal voltage to decrease as current increases.

Question 3

A 12 V battery with an internal resistance of $$1\ \Omega is $$connected to a $$5\ \Omega$$ resistor. What is the power dissipated in the external resistor?

Accepted Answer

$$P = 10.0\ 	ext{W}$$

Question 4

If two resistors, $$R_1 = 2$$\ \Omega$$ and R_2$ = 4\ \Omega$$, are connected in series to a $$12\ 	ext{V}$$ battery (with negligible internal resistance), what is the voltage drop across $$R_2$$?

Accepted Answer

$$V_{R_2$} = 8\ 	ext{V}$$

Question 5

Which equation correctly expresses the electric power $$P$$ delivered to a resistor $$R by a $$current $$I$$?

Accepted Answer

$$P = I^2$ R$$

Question 6

A light bulb is rated at 60 W when connected to a 120 V source. What is the resistance of the bulb's filament when operating at this power?

Accepted Answer

$$R = 240\ \Omega$$

Question 7

If three identical resistors are connected in parallel to a battery, how does the total current drawn from the battery compare to the current through one resistor?

Accepted Answer

The total current is three times the current through one resistor.

Question 8

A circuit consists of a 9 V battery, a $$2\ \Omega$$ internal resistance, and a $$10\ \Omega$$ external resistor. What is the terminal voltage of the battery when the circuit is closed?

Accepted Answer

$$V_{	ext{terminal}} = 7.5\ 	ext{V}$$

Question 9

Which of the following statements about power dissipation in a resistor is correct?

Accepted Answer

Power is maximized when the resistance matches the internal resistance of the battery.

Question 10

A $$24\ 	ext{V}$$ battery with an internal resistance of $$2\ \Omega is $$connected to a $$10\ \Omega$$ resistor. What is the energy dissipated in the resistor after 5 minutes?

Accepted Answer

$$E = 2,400\ 	ext{J}$$

Question 11

If a battery's emf is $$V_0$$ and its internal resistance is $$r$$, what is the maximum current the battery can supply?

Accepted Answer

$$I_{	ext{max}} = \frac{V_0$}{r}$$

Question 12

A student connects a light bulb to a battery and observes that the bulb is dimmer than expected. Which of the following could explain this observation?

Accepted Answer

The battery has significant internal resistance.

Question 13

Which of the following is the correct expression for the total resistance $$R_{	ext{eq}} of $$two resistors $$R_1$$ and $$R_2 in $$parallel?

Accepted Answer

$$R_{	ext{eq}} = \frac{R_1$ R_2$}{R_1$ + R_2$}$$

Question 14

A $$100\ \Omega$$ resistor is connected to a $$10\ 	ext{V}$$ battery. How much energy is dissipated in the resistor in 2 minutes?

Accepted Answer

$$E = 120\ 	ext{J}$$

Question 15

Which of the following best describes the effect of increasing the resistance in a simple circuit powered by a fixed voltage source?

Accepted Answer

The current decreases and the power dissipated decreases.

Electric Power and Resistor Circuits

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