Due: See Website for Due Dates

Problem Set 28

Due: See website for due dates

Chapter 28: Circuits

Problems: 4, 5, 11 (challenging), 39, 42,52, 54, 59, 62, 65

Question A

Explain why an ideal ammeter would have zero resistance and an ideal voltmeter infinite resistance?

Question B

Why do the lights on a car become dimmer when the starter is operated?

Question C

Why does current follow the path of least resistance in a parallel circuit?

Question D

Fish like electric eels have specially designed nerve cells that allow them to discharge hundreds of volts of electricity.Now, while pure water is usually nonconductive, the dissolved salts and other stuff in both sea and fresh water allow them to be conductive. If an electric fish is able to use its electricity to stun enemies or prey, how come the fish itself is unaffected? Hint: think parallel circuit.

Question E

The velocity of the electrons in the wires is very slow (few mm/s), but when one turns on the light, one doesn't see any delay. Why?

Problem 28.4

a. What are the magnitude and direction of the current in the10Ω resistor in the figure?

b. Draw a graph of the potential as a function of the distancetraveled through the circuit, traveling CW from V = 0 V atthe lower left corner.

Answer: −0.9 A

Problem 28.5

a. What are the magnitude and direction of the current in the 18 Ω resistor in the figure?

b. Draw a graph of the potential as a function of the distance traveled through the circuit, traveling CW from V = 0 V at the lower left corner.

Answer: +0.5 A

Problem 28.11 (Challenging)

The five identical bulbs in the figure are all glowing. Thebattery is ideal. What is the order of brightness of the bulbs, frombrightest to dimmest? Some may be equal.

A. P = T Q = R = S

B. P Q = R = S T

C. P = T Q R = S

D. P Q T R = S

Hint: setup a table of bulb, voltage, and power to organize theinformation.

Problem 28.39

It seems hard to justify spending $5 for a compact fluorescentlightbulb when an ordinary incandescent bulb costs 50¢. To seeif this makes sense, compare a 60 W incandescent bulb lasting1000 hours to a 15 W compact fluorescent bulb having a lifetimeof 10,000 hours. Both bulbs produce the same amountof visible light and are interchangeable. If electricity costs$0.10/kWh, what is the total cost—purchase plus energy—toobtain 10,000 hours of light from each type of bulb? This iscalled the life-cycle cost.

Answer: $60.50, $20

Problem 28.42

An electric eel develops a 450 V potential difference betweenits head and tail. The eel can stun a fish or other prey by usingthis potential difference to drive a 0.80 A current pulse for 1.0 ms.What are (a) the energy delivered by this pulse and (b) the totalcharge that flows?

Answer: 0.36 J, 0.80 mC

Problem 28.52

The ammeter in the figurereads 3.0 A. Find I1, I2, and ε.

Answer: 5.0 A, 8.0 A, 14 V

Problem 28.54

For an ideal battery (r = 0 Ω), closing the switch in the figuredoes not affect the brightness of bulb A. In practice, bulb A dimsjust a little when the switch closes. To see why, assume that the1.50 V battery has an internal resistance r = 0.50 Ω and that theresistance of a glowing bulb is R = 6.00 Ω.

a. What is the current through bulb A when the switch is open?

b. What is the current through bulb A after the switch hasclosed?

c. By what percentage does the current through A change whenthe switch is closed?

Answer: 3 A

Problem 28.59

For the circuit shown in the figure, find the current throughand the potential difference across each resistor. Place yourresults in a table for ease of reading.

Answer: 8 V, 16 V, 4A, 2 A, 4/3 A, 2/3 A

Problem 28.62

For the circuit shown in the figure, find the currentthrough and the potential difference across each resistor. Placeyour results in a table for ease of reading.

Answer:(6, 3, 15/4, 9/4) V, (1/4, 1, ¾, 9/16, 9/48) A

Problem 28.65

A 12 V car battery dies not so much because its voltage dropsbut because chemical reactions increase its internal resistance.A good battery connected with jumper cables can both start theengine and recharge the dead battery. Consider the automotivecircuit shown in the figure.

a. How much current could the good battery alone drive throughthe starter motor?

b. How much current is the dead battery alone able to drivethrough the starter motor?

c. With the jumper cables attached, how much current passesthrough the starter motor?

d. With the jumper cables attached, how much current passesthrough the dead battery, and in which direction?

Answer: 200 A, 15 A, 200 A, 4 A