Homework

1
Homework

• P. 526 21, 24, 25

2
Parallel Circuit

• More than one path for the flow of charge
• More room for the flow of charge so Resistance
  goes down
• Voltage must stay the same since all sections
  have the same drop

3
Kirchoffs Junction Rule

• Conservation of charge

4
Kirchoffs Loop Rule

• Conservation of Energy
• The sum of the changes in potential around any
  closed path (loop) of a circuit must be zero.

5

• Parallel Circuit
• Voltmeters are parallel to the circuit

How do the sum of I1, I2, and I3 relate to
IT? Hint What is current? What is it made up
of?
IT
IT
I2 I3
I1
R3
R1
R2
V2
V3
V1
V
V
V
V
V
V
IT
6

• Parallel Circuit
• Voltmeters are parallel to the circuit

IT I1 I2 I3 by Conservation of charge
(conservation of matter)
IT
IT
I2 I3
I1
R3
R1
R2
V2
V3
V1
V
V
V
V
V
V
IT
7

• Parallel Circuit
• Follow the current
• Now map the current flow for circuit 2

IT
R5
R6
R4
V2, I2
V3, I3
R1
R2
V1, I1
R3
IT
Circuit 2
Circuit 1
8

• Parallel Circuit
• Follow the current
• How does circuit 1 differ from circuit 2?

IT
R5
R6
R4
V2, I2
V3, I3
R1
R2
V1, I1
R3
IT
9
R1 100 Ohms
VT 120V
R2 200 Ohms
V1
VT
V2
RT
V2, I2
V
V
V1, I1
R1
R2
IT
IT
I1
I2
10
R1 100 Ohms
VT 120V
R2 200 Ohms
V1
R3 150 Ohms
V2
VT
RT
V3
V2, I2
V3, I3
V
V
R3
V1, I1
R1
R2
IT
IT
I1
I2
I3
11
R1
VT 120V
Rwire 1 Ohms
R2
V1
R3
V2
VT
RT
V3
V2, I2
V3, I3
V
V
R3
V1, I1
R1
R2
IT
IT
I1 5A (600W)
I2 5A
I3 5A
12
For parallel circuits
From Ohms law
V is the same
Substituting,
yielding
13
Electrical Power

• Power is the rate at which work is done or energy
  is expended.
• Unit is Watt Joule / second
• (James Watt worked on steam engines and launched
  the industrial revolution)
• Power Work / time
• Electrical Energy Power Time VIt

14
Electrical Power

• P IV Poison Ivy
• Watts J/sec Coulomb/sec J/C
• V W/q Joules/Coulomb

15
Electrical Power

• Power is the rate at which a charge is moved
  through a potential difference
• Power Current Voltage
• (Coulombs/sec) (Joules / Coulomb)
• Joules / second
• Electrical Energy Power time P t

16
Electrical Power

• P IV Poison Ivy
• What if I only have I and R?

17
Electrical Power

• P IV Poison Ivy
• What if I only have I and R?
• V IR

18
Electrical Power

• P IV Poison Ivy
• What if I only have I and R?
• V IR
• P IV I (IR) I2R

19
Electrical Power

• P IV Poison Ivy
• What if I only have I and R?
• V IR
• P IV I (IR) I2R (I2R losses)
• What if I only have V and R?

20
Electrical Power

• P IV Poison Ivy
• What if I only have I and R?
• V IR
• P IV I (IR) I2R
• What if I only have V and R?
• P IV V (V/R) V2/R

21
Electrical Power

• P IV I2R V2/R

22
Examples

• Dante has a 5A fuse in line with his car radio (a
  12V supply). What is the maximum power his
  speakers can handle without blowing the fuse?
• Mr. Daviss antique electric heater is rated at
  1350W.
• For a 120V supply, what is the current?
• What is the resistance?

23
Examples

• Given a 60W light bulb in a 120V circuit, how
  much current does it draw?
• What is its resistance?
• Given a stove with a burner having a 20W
  resistance
• How much power is developed with a 120V supply?
  How much current?
• How much power is developed with a 240V supply?
  How much current?

24
Examples

• The power lines leading to a house typically
  support 200A at 220V.
• How much power is the maximum available?
• If the wire leading to the house has a resistance
  of 14W, how much power is lost in the wiring?
• The voltage in the neighborhood is typically
  7200V. For the same 14W wire and household
  power, how much power is lost in the wire?
• Why do utilities like to use high voltage lines?

25
Electrical Energy

• Electrical Energy
• Follows the same conservation laws as all other
  forms of energy
• Potential energy (charge at a high potential)
• Converts to kinetic energy (via a motor)
• Converts to thermal energy (via resistance)

26
Electrical Energy

• Electrical Energy is priced in kWh
• One kiloWatt 1000 Watts
• One kWh One kW for one hour

27
Electrical Energy

• Electrical Energy PowerTime Pt VIt
• Electrical energy has units of Joules
• 3,600,000 Joules
• 1000 Joules / sec 3600 seconds
• 1000 Watts 1 hour 1kiloWatt-hour
• 1 kWh 0.13

28
Electrical Energy

• Hand Generator

29
Examples

• Given a 60W light bulb in a 120V circuit, how
  much current does it draw?
• What is its resistance?
• How many kWh does it consume in 8 hours?
• How much does this cost at 0.13/kWh?
• Given a stove with a burner having a 20W
  resistance
• How much power is developed with a 120V supply?
  How much current?
• How much power is developed with a 240V supply?
  How much current?

30
Resistance of an object

• What would we expect it to depend on?
• (Resistance is the impedance to the flow of
  charge)

31
Resistance of an object

• What would we expect it to depend on?
• (Resistance is the impedance to the flow of
  charge)

L
A
32
Find Resistance of a material

• Depends on four factors
• R 8 Temp
• R 8 RHO (?) resitivity
• R 8 Length
• R 8 A-1 (cross-sectional Area)

33
Low resistance

• Short
• Fat
• cold

34
High Resistance

• Long
• Thin
• Hot

35
Series and Parallel Circuits
L
Series Single Path, high effective resistance
a
L
A
Parallel Multiple Paths, low effective
resistance
36
Resistivities at 20C Resistivities at 20C
Material Resistivity
Aluminum 2.82 108
Copper 1.72 108
Gold 2.44 108
Nichrome 150. 108
Silver 1.59 108
Tungsten 5.60 108
From Reference tables
37
(No Transcript)
38
Monthly Service Charge is 18 Monthly Service Charge is 18
Central Hudson Variable Costs Central Hudson Variable Costs Central Hudson Variable Costs

0.047
0.002
-0.007
0.004
0.001
0.003
0.001
0.004
0.065
0.014

Total 0.134

39
Monthly Charges Monthly Charges Monthly Charges (Includes the effect of Schedules 59, 91, 93)
6.00 Basic Charge, Basic Charge, plus
0.06850 0.06850 per Kwh for the first per Kwh for the first per Kwh for the first 600 Kwhs
0.07933 0.07933 per Kwh for the next per Kwh for the next per Kwh for the next 700 Kwhs
0.09260 0.09260 per Kwh for all additional Kwhs per Kwh for all additional Kwhs per Kwh for all additional Kwhs per Kwh for all additional Kwhs

Example - Example -                  
  If you used 1450 1450 Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this Kwhs of electricity, your bill would be calculated like this  
  Basic Charge 6.00  
  0.06850 0.06850 x 600 Kwhs 41.100  
  0.07933 0.07933 x 700 Kwhs 55.531  
  0.09260 0.09260 x 150 Kwhs 13.890  
  Charge for 1450 1450 Kwhs 116.52 (franchise fees not included) (franchise fees not included)