Assignment 11: EMF and Power

Due: 8:00am on Wednesday, February 15, 2012

Note: To understand how points are awarded, read your instructor's Grading Policy.

Power in Resistive Electric Circuits

Learning Goal: To understand how to compute power dissipation in a resistive circuit.

The circuit in the diagram consists of a battery with EMF , a resistor with

resistance , an ammeter, and a voltmeter. The voltmeter and the ammeter (labeled V and A) can be considered

ideal; that is, their resistances are infinity and zero, respectively. The current in the resistor is , and the voltage

across it is . The internal resistance of the battery is not zero.

Part A

What is the ammeter reading ?

Express your answer in terms of , , and .

ANSWER:

=

Correct

Note that the resistances of the ammeter and voltmeter do not appear in the answer. That is because these two

circuit elements are "ideal." The voltmeter has infinite resistance, so no current flows through it (imagine that

there is a short circuit inside the voltmeter). The ammeter has zero resistance, so there is no voltage drop as

current flows through it.

Part B

What is the voltmeter reading ?

Hint B.1 Potential difference across the internal resistance

Hint not displayed

Express your answer in terms of , , and .

ANSWER:

=

Correct

In the following parts, you will express the power dissipated in the resistor of resistance using three different sets

of variables.

Part C

What is the power dissipated in the resistor?

Express your answer in terms of and .

ANSWER:

=

Correct

Part D

Again, what is the power dissipated in the resistor?

This time, express your answer in terms of one or more of the following variables: , , and .

ANSWER:

=

Correct

Part E

For the third time, what is the power dissipated in the resistor?

Express your answer in terms of one or more of the following variables: , , and .

ANSWER:

=

Correct

Part F

What is the total power dissipated in the resistive elements of the circuit?

Hint F.1 How to approach the problem

Hint not displayed

Hint F.2 Find the power dissipated in the battery

Hint not displayed

Hint F.3 Find the power dissipated between points 1 and 2

Hint not displayed

Express your answer in terms of one or more of the following variables: , , and .

ANSWER:

=

Correct

Part G

What is the total power dissipated in the resistive elements of the circuit, in terms of the EMF of the battery

and the current in the circuit?

Express your answer in terms of and the ammeter current .

ANSWER:

=

Correct

± Resistance of a Heater

A 1500-W heater is designed to be plugged into a 120-V outlet.

Part A

What current will flow through the heating coil when the heater is plugged in?

Hint A.1 Setting it up

Hint not displayed

Hint A.2 Power

Hint not displayed

Hint A.3 Finishing up

Hint not displayed

Express your answer for the current numerically, to three significant figures.

ANSWER:

=

12.5

Correct A

Note that watts/volts has the correct units: Since

and

,

then

.

Part B

What is , the resistance of the heater?

Hint B.1 Which equation to use

Hint not displayed

Express your answer numerically, to three significant figures.

ANSWER:

=

9.6

Correct ohms

Part C

How long does it take to raise the temperature of the air in a good-sized living room by ?

Note that the specific heat of air is 1006 and the density of air is .

Hint C.1 Mass of the air

Hint not displayed

Hint C.2 How many joules

Hint not displayed

Express your answer numerically in minutes, to three significant figures.

ANSWER:

=

16.1

Correct minutes

Actually, the heat capacity of the walls and other material in the room will generally exceed that of the air by

several times, so an hour is a more reasonable time to heat the room by this much.

Measuring the EMF and Internal Resistance of a Battery

When switch S in the figure is open, the voltmeter V of the battery reads 3.12 . When the switch is closed, the

voltmeter reading drops to 2.96 , and the ammeter A reads 1.66 . Assume that the two meters are ideal, so they

do not affect the circuit.

Part A

Find the emf .

Express your answer in volts to three significant digits.

ANSWER:

=

3.12

Correct

Part B

Find the internal resistance of the battery.

Hint B.1 How to approach the problem

Hint not displayed

Express your answer in ohms to four significant digits.

ANSWER:

=

9.639×10−2

Correct

Part C

Find the circuit resistance .

Hint C.1 Find the voltage drop across the circuit resistor

Hint not displayed

Express your answer in ohms to three significant digits.

ANSWER:

=

1.78

Correct

This is the kind of circuit you would use in real life to measure the emf and internal resistance of a battery. You

need the second resistor to increase the resistance in the circuit so that the current flowing through the ammeter

is not too large. In fact, you would need to figure out roughly how big a resistance to use once you had

determined the emf of the battery, depending on the range of the ammeter you were using.

Exercise 25.32

The circuit shown in the figure contains two batteries, each with an emf

and an internal resistance, and two resistors.

Part A

Find the magnitude of the current in the circuit.

Express your answer using two significant figures.

ANSWER:

=

0.47

Correct

Part B

Find the direction of the current in the circuit.

ANSWER:

counterclockwise

clockwise

Correct

Part C

Find the terminal voltage of the 16.0- battery.

Express your answer using two significant figures.

ANSWER:

=

15

Correct

Part D

Find the potential difference of point with respect to point .

Express your answer using two significant figures.

ANSWER:

=

11

Correct

Exercise 25.52

A typical small flashlight contains two batteries, each having an emf of 1.50 connected in series with a bulb

having a resistance of 19 .

Part A

If the internal resistance of the batteries is negligible, what power is delivered to the bulb?

Express your answer using two significant figures.

ANSWER:

=

0.47

Correct

Part B

If the batteries last for a time of 4.5 , what is the total energy delivered to the bulb?

Express your answer using two significant figures.

ANSWER:

=

7700

Correct

Part C

The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is

the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial

value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat when the current

through the filament changes, because this changes the temperature of the filament and hence the resistivity of

the filament wire.)

Express your answer using two significant figures.

ANSWER:

=

7.9

Correct

Problem 25.80

A lightning bolt strikes one end of a steel lightning rod, producing a 15100-A current burst that lasts for 60 . The

rod is 2.2 long and 1.6 in diameter, and its other end is connected to the ground by 30 of 8.3-mm-diameter

copper wire.

Part A

Find the potential difference between the top of the steel rod and the lower end of the copper wire during the

current burst.

Express your answer using two significant figures.

ANSWER:

=

180

Correct

Part B

Find the total energy deposited in the rod and wire by the current burst.

Express your answer using two significant figures.

ANSWER:

=

160

Correct

Measuring Temperature Using a Carbon Resistor

Part A

A carbon resistor is to be used as a thermometer. On a winter day when the temperature is 4.00 , the resistance

of the carbon resistor is 217.4 . What is the temperature on a spring day when the resistance is 215.0 ?

Hint A.1 Formula for the temperature dependence of resistance

Hint not displayed

Take the temperature coefficient of resistivity for carbon to be = −5.00×10−4

.

ANSWER:

26.1

Correct

This problem demonstrates how you might use a resistor as a thermometer. Since resistors are typically made of

metal or carbon, these thermometers are physically more robust compared to mercury thermometers, and they can

be used where temperatures are below the freezing point or above the boiling point of mercury (depending on the

material the resistor is made of).

Problem 25.68

Part A

What is the potential difference in the circuit of the figure?

ANSWER:

=

6.58

Correct

Part B

What is the terminal voltage of the 4.00- battery?

ANSWER:

=

4.08

Correct

Part C

A battery with emf 10.30 and internal resistance 0.50 is inserted in the circuit at , with its negative terminal

connected to the negative terminal of the 8.00- battery. What is the difference of potential between the

terminals of the 4.00- battery now?

ANSWER:

=

3.87

Correct