Homework P , 24, 25

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

Kirchoff’s Junction Rule Conservation of charge

Kirchoff’s Loop Rule Conservation of Energy The sum of the changes in potential around any closed path (loop) of a circuit must be zero.

R3R3 V2V2 A VV ITIT R1R1 A ITIT R2R2 VVVV V3V3 V1V1 Parallel Circuit: V oltmeters are parallel to the circuit I1I1 I 2 + I 3 ITIT How do the sum of I1, I2, and I3 relate to IT? Hint: What is current? What is it made up of? A AA

R3R3 V2V2 A VV ITIT R1R1 A ITIT R2R2 VVVV V3V3 V1V1 Parallel Circuit: V oltmeters are parallel to the circuit I1I1 I 2 + I 3 ITIT I T = I 1 + I 2 + I 3 by Conservation of charge (conservation of matter)

R5R5 A ITIT R1R1 A ITIT R2R2 Parallel Circuit: Follow the current Now map the current flow for circuit 2 V 1, I 1 V 3, I 3 V 2, I 2 R3R3 R6R6 R4R4 A Circuit 2Circuit 1

R5R5 A ITIT R1R1 A ITIT R2R2 Parallel Circuit: Follow the current How does circuit 1 differ from circuit 2? V 1, I 1 V 3, I 3 V 2, I 2 R3R3 R6R6 R4R4 A

A ITIT R1R1 R 1 = 100 Ohms R2R2 V 2, I 2 V 1, I 1 VV VTVT R 2 = 200 Ohms I T = I 1 = I 2 = V T = 120V V 1 = V 2 = R T =

A ITIT R1R1 VTVT R2R2 V 3, I 3 V 2, I 2 R3R3 V 1, I 1 VV I T = I 1 = I 3 = V T = 120V V 1 = V 3 = R 1 = 100 Ohms R T = R 2 = 200 Ohms V 2 = I 2 = R 3 = 150 Ohms

A ITIT R1R1 VTVT R2R2 V 3, I 3 V 2, I 2 R3R3 V 1, I 1 VV I T = I 1 = 5A (600W) I 3 = 5A V T = 120V V 1 = V 3 = R wire = 1 Ohms R T = R 2 = V 2 = I 2 = 5A R 3 = R 1 =

yielding For parallel circuits From Ohm’s law V is the same Substituting,

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

Electrical Power P= IV “Poison Ivy” Watts = J/sec = Coulomb/sec * J/C V = W/q = Joules/Coulomb

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

Electrical Power P= IV “Poison Ivy” What if I only have I and R?

Electrical Power P= IV “Poison Ivy” What if I only have I and R? V = IR

Electrical Power P= IV “Poison Ivy” What if I only have I and R? V = IR P = IV = I (IR) = I 2 R

Electrical Power P= IV “Poison Ivy” What if I only have I and R? V = IR P = IV = I (IR) = I 2 R (I 2 R losses) What if I only have V and R?

Electrical Power P= IV “Poison Ivy” What if I only have I and R? V = IR P = IV = I (IR) = I 2 R What if I only have V and R? P = IV = V * (V/R) = V 2 /R

Electrical Power P= IV = I 2 R = V 2 /R

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. Davis’s antique electric heater is rated at 1350W. – For a 120V supply, what is the current? –What is the resistance?

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 20  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?

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 14 , how much power is lost in the wiring? The voltage in the neighborhood is typically 7200V. For the same 14  wire and household power, how much power is lost in the wire? –Why do utilities like to use high voltage lines?

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)

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

Electrical Energy Electrical Energy = Power*Time = 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

Electrical Energy –Hand Generator

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 20  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?

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

Resistance of an object What would we expect it to depend on? (Resistance is the impedance to the flow of charge) A L

Find Resistance of a material Depends on four factors –R ∞ Temp –R ∞ RHO (ρ) resitivity –R ∞ Length –R ∞ A -1 (cross-sectional Area)

Low resistance Short Fat cold

High Resistance Long Thin Hot

Series and Parallel Circuits a L A L Parallel: Multiple Paths, low effective resistance Series: Single Path, high effective resistance

Resistivities at 20°C MaterialResistivity Aluminum2.82 × 10–8 Copper1.72 × 10–8 Gold2.44 × 10–8 Nichrome150. × 10–8 Silver1.59 × 10–8 Tungsten5.60 × 10–8 From Reference tables

Monthly Service Charge is $18 Central Hudson Variable Costs $0.047 $ $0.007 $0.004 $0.001 $0.003 $0.001 $0.004 $0.065 $0.014 Total$0.134

Monthly Charges – (Includes the effect of Schedules 59, 91, & 93) $6.00Basic Charge,plus $ per Kwh for the first600Kwhs $ per Kwh for the next700Kwhs $ per Kwh for all additional Kwhs Example - If you used1450 Kwhs of electricity, your bill would be calculated like this: Basic Charge=$6.00 $ x600Kwhs=$ $ x700Kwhs=$ $ x150Kwhs=$ Charge for1450Kwhs=$ (franchise fees not included)