11/30/2018 HW4

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HW4 Due: 11:59pm on Thursday, October 25, 2018

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Exercise 25.16

Part A

A ductile metal wire has resistance . What will be the resistance of this wire in terms of if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched. (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)

ANSWER:

Conceptual Question 25.01

Part A

The figure shows a steady electric current passing through a wire with a narrow region. What happens to the drift velocity of the moving charges as they go from region to region and then to region ?

ANSWER:

Conceptual Question 25.03

Part A

R R

= R1 R

A B C

The drift velocity increases all the time.

The drift velocity decreases all the time.

The drift velocity remains constant.

The drift velocity increases from A to B and decreases from B to C.

The drift velocity decreases from A to B and increases from B to C.

11/30/2018 HW4

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The figure shows two connected wires that are made of the same material. The current entering the wire on the left is 2.0 A and in that wire the electron drift speed is d. What is the electron drift speed in the wire on the right side?

ANSWER:

Conceptual Question 25.10

Part A

Two cables of the same length are made of the same material, except that one cable has twice the diameter of the other cable. When the same potential difference is maintained across both cables, which of the following statements are true? (There may be more than one correct choice.)

Choose all that apply.

ANSWER:

Prelecture Concept Question 25.01

Part A

Which of the following statements are true?

v

dv

4 dv

d/2v

2 dv

d/4v

Both cables carry the same current density.

The electrons have the same drift velocity in both cables.

The current in the thin cable is four times as great as the current in the thick cable.

The same current flows through both cables.

The current in the thin cable is twice as great as the current in the thick cable.

11/30/2018 HW4

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Check all that apply.

ANSWER:

Prelecture Concept Question 25.05

Part A

Consider two copper wires with the same cross-sectional area. Wire A is twice as long as wire B. How do the resistivities and resistances of the two wires compare?

Check all that apply.

ANSWER:

Prelecture Concept Question 25.09

Part A

A circuit maintains a constant resistance. If the current in the circuit is doubled, what is the effect on the power dissipated by the circuit?

ANSWER:

A battery does work on electric charges to bring them to a position of higher electric potential energy so that they can flow through a circuit to a lower potential energy.

The potential difference between the terminals of a battery, when no current flows to an external circuit, is referred to as the terminal voltage.

The internal resistance of a battery decreases with decreasing temperature.

A battery is a device that produces electricity by transforming chemical energy into electrical energy.

Wire A has twice the resistance of wire B.

Wire B has twice the resistance of wire A.

Wire A and wire B have the same resistance.

Wire A and wire B have the same resistivity.

Wire B has twice the resistivity of wire A.

Wire A has twice the resistivity of wire B.

11/30/2018 HW4

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Problem 25.16

Part A

The resistivity of gold is 2.44×10-8 Ω•m at room temperature. A gold wire that is 1.4 mm in diameter and 39 cm long carries a current of 950 mA. What is the electric field in the wire?

ANSWER:

Problem 25.24

Part A

A Nichrome wire is used as a heating element in a toaster. From the moment the toaster is first turned on to the moment the wire reaches it maximum temperature, the current in the wire drops by 20.0% from its initial value. What is the temperature change in the wire? The temperature coefficient of resistivity for Nichrome is 0.000400 (°C)-1.

ANSWER:

The power dissipated is reduced by a factor of 2.

The power dissipated remains constant.

The power dissipated is doubled.

The power dissipated is reduced by a factor of 4.

The power dissipated is quadrupled.

3.8×10−3 V/m

1.2×10−2 V/m

1.5×10−2 V/m

1.9×10−2 V/m

3.8×10−2 V/m

11/30/2018 HW4

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Problem 25.26

Part A

A piece of wire 41.5 cm long carries a current I when a voltage V is applied across its ends at a temperature of 0°C. If the resistivity of the material of which the wire is made varies with temperature as shown in the graph in the figure, what length of the same diameter wire is needed so that the same current flows when the same voltage is applied at temperature 400°C?

ANSWER:

Problem 25.29

Part A

When a voltage difference is applied to a piece of metal wire, a 4-mA current flows through it. If this metal wire is now replaced with a silver wire having twice the diameter of the original wire, how much current will flow through the silver wire? The lengths of both wires are the same, and the voltage difference remains unchanged. (The resistivity of the original metal is 1.68 × 10-8 Ω · m, and the resistivity of silver is 1.59 × 10-8 Ω · m.)

ANSWER:

625°C

200°C

300°C

400°C

500°C

cm

11/30/2018 HW4

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Problem 25.38

Part A

The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated with a current that is 50% of the current rating of the bulb, what is the actual power drawn by the bulb?

ANSWER:

Problem 25.44

Part A

In the figure a current of 6.0 A is drawn from the battery. What is the terminal voltage Vab of the battery?

ANSWER:

17 mA

8.5 mA

15 mA

4.2 mA

30 W

20 W

10 W

25 W

15 W

11/30/2018 HW4

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Problem 25.56

A heating element made of tungsten wire is connected to a large battery that has negligible internal resistance. When the heating element reaches 80.0 , it consumes electrical energy at a rate of 420 . Assume that the temperature coefficient of resistivity has the value given in Table 25.2 in the textbook and that it is constant over the temperature range in this problem. In the equation

take to be 20.0 .

Part A

What is its power consumption when the temperature of the heating element is 110.0 ?

Express your answer to two significant figures and include the appropriate units.

ANSWER:

Problem 25.58

A resistor with resistance is connected to a battery that has emf 16.0 and internal resistance = 0.350 .

Part A

For what two values of will the power dissipated in the resistor be 78.0 ?

Enter your answers separated by a comma.

ANSWER:

Problem 25.70

Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 incandescent bulb uses only 23.0 of power. The compact bulb lasts 1.00×104 hours, on

0.00 V

-24 V

+24 V

+12 V

-12 V

C∘ W

R(T ) = [1 + α(T − )]R0 T0

T0 C ∘

C∘

= P

R V r Ω

R W

, = R1 R2 Ω

W W

11/30/2018 HW4

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the average, and costs 12.0 , whereas the incandescent bulb costs only 74.0 ¢, but lasts just 750 hours. The study assumed that electricity cost 7.00 ¢ per and that the bulbs were on for 4.0 per day.

Part A

What is the total cost (including the price of the bulbs) to run incandescent bulbs for 3.0 years?

ANSWER:

Part B

What is the total cost (including the price of the bulbs) to run compact fluorescent bulbs for 3.0 years?

ANSWER:

Part C

How much do you save over 3.0 years if you use a compact fluorescent bulb instead of an incandescent bulb?

ANSWER:

Part D

What is the resistance of a “100 ” fluorescent bulb? (Remember, it actually uses only 23 of power and operates across 120 .)

ANSWER:

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$ kWh h

dollar(s)

dollar(s)

dollar(s)

W W V

= R Ω