# Physics

A nichrome cable has a current of 140 A running through

it. Between two points on the cable that are 0.22 m apart, there is a potential difference of 0.036 V (a) Calculate the diameter of the cable. (b) How much heat energy does this part of the wire emit in 1 minute?

8) A “Rockstar” toaster uses a

tungsten heating element (wire). The wire has a diameter of 1.2 mm. When the toaster is turned on at 20° C, the initial current is 1.6 A. (a) What is the current density in the wire? (b) A few seconds later, the toaster heats up and the current is 1.20 A. What is the temperature of the wire? (c) If the toaster is plugged into a standard wall outlet in Kankakee, Illinois, what is the rate that energy is dissipated from the heating element?

9) Skid runs a 10 mile line of copper cable out to his shack in

the sticks so he can have electricity to play Lord of the Rings Online. At 20ºC the resistance of the cable is 12 Ω. At 50ºC the cable emits 1.5 kJ every second. (a) What is the resistance of the cable at 50ºC? (b) What is the current running through the cable at 50ºC? (c) Calculate the current density at 50ºC.

C1 = 18 μF

Wire #1 Wire #2 C2 = 6 μF

C3 = 4 μF

C4 = 30 μF 25 V

C1 = 5 μF C2 = 4 μF

C3 = 1 μF

C4 = 12 μF

15 V

10) A modern hair dryer uses a nichrome heating element that typically is 30-gauge wire around 40 cm in length. The gauge rating on a wire refers to its diameter. In this case, 30-gauge wire has a diameter of 0.254 mm. Nichrome has a number density of 7.94 x 1028 e–/m3. If the drift velocity of the electrons in the wire is 18.7 mm/s, what is the voltage that the hair dryer is plugged into?

11) Before LCD, LED, Plasma,

and (the latest) OLED TVs, there were CRT (Cathod-Ray Tube) TVs. Inside these TVs were electron guns that shot an electron beam of diameter 0.5 mm and current density of 244 A/m2 onto the inside of a glass screen which was coated with phosphor. How many electrons would hit the phosphor every minute?

12)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

13)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

14)

Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.

15) Design a circuit that has an equivalent resistance of

1.00 Ω using at least one of each of the following resistors: a 1 Ω, a 2 Ω, and a 6 Ω. [You must also show where your A and B terminals are located.]

ANSWERS:

NOTE: Some of these answers are minimal since there are checks that you can do to verify your answers.

A

27 Ω

B 54 Ω

8 Ω

30 Ω

16 Ω

14 Ω

10 Ω

30 Ω

B

18 Ω

96 Ω

6 Ω

32 Ω 18 Ω

60 ΩA

A

20 Ω

30 Ω

B

30 Ω

7 Ω

50 Ω

12 Ω

45 Ω

60 Ω

1) CEQ = 18 μF 8) a) 1.415 x 106 A/m2

2) CEQ = 6 μF b) 94.1ºC 3) CEQ = 2 μF c) 144 W

9) a) 13.4 Ω 4) a) 0.444 A b) 2.96 mm b) 10.58 A

c) 5.14 x 105 A/m2 5) a) 1.13 x 1014 p+/m3 b) 5.63 x 1017 p+ 10) 95.0 V 6) 0.262 mm/s 11) 1.8 x 1016 e–

7) a) 0.033 m 12) 4 Ω b) 302 J 13) 14 Ω 14) 22 Ω

Physics 226 Fall 2013

Problem Set #9

NOTE: You can only use circuit tricks on 9 – 11 but not on any others. 1) Analyze the following circuit using a VIR chart. 2) Swap the location of the battery and R1 in the circuit from

problem #1. Analyze the circuit using a VIR chart. 3) Analyze the following circuit using a VIR chart. 4) The battery in this problem has an internal resistance of

0.15 Ω. (a) Analyze the following circuit using a VIR chart. (b) Is this circuit well designed? Discuss, explain.

5) Analyze the following circuit using a VIR chart.

6) Analyze the following circuit using a VIR chart. 7) The battery in this problem has an internal resistance of

1 Ω. (a) Analyze the following circuit using a VIR chart. (b) Is this circuit well designed? Discuss, explain.

8) A load of 3.5 Ω is connected across a 12 V battery. You

measure a voltage of 9.5 V across the terminals of the battery. (a) Find the internal resistance of the battery. (b) Is this circuit well designed? Discuss, explain.

9) Analyze the circuit from problem

#5 using a VIR chart. You are using only the diagram in #5, not the values. New values are given at the right. You may use a circuit trick for this circuit, but only for ONE value.

10) Analyze the circuit from problem

#6 using a VIR chart. You are using only the diagram in #6, not the values. New values are given at the right. You may use a circuit trick for this circuit, but only for ONE value.

R1

20 V

R2 R3 R4

R5

Given: R1 = 12 Ω R2 = 3 Ω R3 = 8 Ω R4 = 36 Ω R5 = 15 Ω

50 V

R1 Given: R1 = 28 Ω R2 = 6 Ω R3 = 84 Ω R4 = 7 Ω R5 = 54 Ω

R3

R2

R4

R5

55 V

R1 Given: R1 = 18 Ω R2 = 32 Ω R3 = 15 Ω R4 = 21 Ω R5 = 42 Ω R6 = 30 Ω R7 = 52 Ω

R3

R2

R4 R5

R6 R7

R1

VB

R2

R3 R4

Given: VB = 60 V V2 = 50 V

I1 = 2 A I4 = 3 A

R3 = 8 Ω

R1

VB

R2 R3

R4

R5

Given: V5 = 32 V

I2 = 0.4 A I4 = 0.5 A

R1 = 36 Ω R6 R3 = 60 Ω R4 = 36 Ω R6 = 32 Ω

Given: R1

VB

VB = 32 V V2 = 16 V R2 R3

I1 = 4 A

R3 = 12 Ω R4 R4 = 8 Ω

Given: VB = 63 V R1 = 8 Ω R2 = 20 Ω R3 = 35 Ω R4 = 49 Ω

Given: VB = 75 V R1 = 16 Ω R2 = 40 Ω R3 = 48 Ω R4 = 24 Ω R5 = 8 Ω R6 = 24 Ω

11) Analyze the following circuit using a VIR chart. 12) Using the information you are

given for the circuit at the right, answer the following. (a) Determine the magnitude and direction of the current in the circuit. (b) Determine which point, A or B, is at a higher potential.

13) Calculate the unknown currents I1, I2, and I3 for the circuit

below.

14) Calculate the unknown currents I1, I2, and I3 for the circuit below.

Given: 15) Calculate the unknown currents I1, I2, and I3 for the circuit

below.

ANSWERS:

NOTE: These answers are minimal since there are checks that you can do to verify your answers.

R1

R3 R4

R5 R6

I1 8 VVB = 50 V

R1 = 9 Ω R2 = 4 Ω R3 = 18 Ω R4 = 4 Ω R5 = 7 Ω R6 = 12 Ω

B

A

17 V

13 Ω 7 Ω

5 Ω

11 Ω

23 V

6 Ω

1 Ω

10 V

25 V

3 Ω

5 Ω

7 Ω

I1

I2

I3

4 Ω

9 Ω

10 Ω

4 Ω 7 Ω

I2

6 Ω

I3 22 V

3 Ω 10 VI1

4 Ω

4 Ω 25 V

2 Ω 5 Ω

I2 I3

20 V4 Ω

7) REQ = 8 Ω 1) REQ = 2 Ω 8) a) 0.923 Ω 2) REQ = 11.48 Ω 9) REQ = 21 Ω 3) REQ = 25 Ω 10) REQ = 25 Ω 4) REQ = 12.15 Ω 11) REQ = 20 Ω 5) REQ = 12 Ω 12) a) 1.11 A 6) REQ = 40 Ω

Physics 226 Fall 2013

Problem Set #10 1) Given the circuit at the right in

which the following values are used: R1 = 6 MΩ, R2 = 12 MΩ, and C = 3 μF. (a) You close the switch at t = 0. Find all voltages and currents for the resistors. (b) After a long time find all voltages and currents for the resistors. (c) At t = 20 s find the voltage across the capacitor. (d) Find the time constant of the capacitor. (e) Find the half- life of the circuit.

2) Given the circuit at below, do the following. (a) Find all

voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors.

3) Given the circuit at below, do the following. (a) Find all

voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors.

4) Given the circuit at below, do the following. (a) Find all

voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors. 24 V

5) Given the circuit at below, do the following. (a) Find all voltages and currents for the resistors at the instant the switch is closed. (b) After the switch has been closed a long time, find all voltages and currents for the resistors.

6) You have a current, I, flowing

through a loop of blue wire of radius, R. (a) Using the current version of the Biot- Savart Law (the cross product form), derive an equation for the total magnetic field at the center of the loop. (b) In what direction does the field point?

R1

R2