Series and Parallel Circuits

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Ohm’s law applies for each circuit element and for the circuit as a whole. + V Electrons have a choice about which path they follow. A IT R1 R2 V2, I2 V1, I1 V VT Electrons must all flow in the same path Series Circuit Parallel Circuit

Electrical Circuits In a series electric circuit, the voltage drops as it flows through each resistive circuit element

Resistors in Series: Building Analogy R1 = Lamp 6 steps R1 R2 = Lamp Elevator (battery) 11 steps R3 = Lamp R2 3 steps To go from the top to the bottom floor, all people must take the same path. So, by definition, the staircases are in series. With each flight people lose some of the potential energy given to them by the elevator, expending all of it by the time they reach the ground floor. So the sum of the V drops across the resistors the voltage of the battery. People lose more potential energy going down longer flights of stairs, so long stairways correspond to high resistance resistors. The double waterfall is like a pair of resistors in series because there is only one route for the water to take. The longer the fall, the greater the resistance.

Diagramming circuits

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.

Series Circuit Current : One path for the flow of charge It = I1 = I2 = I3 Resistance must increase because length increases Rt = R1 + R2 + R3 Voltage must add to Zero Vt - V1 - V2 - V3=0 Vt =V1 + V2 + V3

A V V Name:___________________________________________________ I1 = 1 + V1 = 9 V2 = R2 = V V

V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = Vt = It = Rt = Pt = A V V A V V Name:___________________________________________________ VT = V1 + V2 + V3 + … RT = R1 + R2 + R3 + … IT = I1 = I2 = I3 = … First, fill in all values of V and I. After review, fill in values of R. Assume all light bulbs have the same resistance. I1 = A + Vt = 4 V V L1 V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = Vt = It = Rt = Pt = A I2 = 2 L2 V V

V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = VT = V1 + V2 + V3 + … RT = R1 + R2 + R3 + … IT = I1 = I2 = I3 = … First, fill in all values of V and I. After review, fill in values of R. Assume all light bulbs have the same resistance. IT = 1 A + I2 = V V2 = 3 R2 = VT = I1 = L3 L1 L2 V1 = I1 = R1 = V3 = I3 = R3 = V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = Vt = It = Rt = Pt =

Series Circuit Example VT = V1 + V2 + V3 + … RT = R1 + R2 + R3 + … IT = I1 = I2 = I3 = … Series Circuit Example IT A V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = Vt = It = Rt = Pt = V1 = I1 = R1 = 5W + VT V V A V2 = I2 = 1A R2 = V V Given: Vt = 10V R1 = 5W I2 = 1A P3 = 2W V3 = I3 = R3 = V V

Series Circuit Example VT = V1 + V2 + V3 + … RT = R1 + R2 + R3 + … IT = I1 = I2 = I3 = … IT Series Circuit Example A V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = Vt = It = Rt = Pt = V1 = I1 = R1 = 5W + VA V V A V2 = I2 = 1A R2 = + VB V V Given: VA = 3V VB = 7V R1 = 5W I2 = 1A P3 = 2W V3 = I3 = R3 = V V

V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = VT = V1 + V2 + V3 + … RT = R1 + R2 + R3 + … IT = I1 = I2 = I3 = … IT V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = V4 = I4 = R4 = P4 = Vt = It = Rt = Pt = A V1 = I1 = R1 = 1W V V V2 = I2 = R2 = 2W + VT V V A I5 = V3 = 6V I3 = R3 = 3W V V A I6 = V4 = I4 = R4 = 4W V V

V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = VT = V1 + V2 + V3 + … RT = R1 + R2 + R3 + … IT = I1 = I2 = I3 = … It = V1 = I1 = R1= P1 = V2 = I2 = R2 = P2 = V3 = I3 = R3 = P3 = V4 = I4 = R4 = P4 = Vt = It = Rt = Pt = A V1 = 3 I1 = R1 = V V V2 = I2 = R2 = 2W + Vt = V V A I5 = V3 = 5V I3 = R3 = V V A I6 = V4 = 4V I4 = R4 = 4W V V

Questions What happens if we greatly increase the resistance? When else, besides electricity, do we see things like this? - Think about the effects on voltage (pressure), current (flow), and resistance (blockage)

Tell me about heart bypassess…

Tell me about heart bypassess…

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

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

Voltmeters are parallel to the circuit 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 A I1 R1 R2 R3 V1 V2 V3 V V V V V V A A IT A A

Voltmeters are parallel to the circuit Parallel Circuit: Voltmeters are parallel to the circuit IT = I1 + I2 + I3 by Conservation of charge (conservation of matter) IT IT I2 + I3 A I1 R1 R2 R3 V1 V2 V3 V V V V V V A IT

Kirchoff’s Junction Rule Conservation of charge

Parallel Equations It = I1 + I2 + I3 + … Vt = V1 = V2 = V3 = How do we find the equivalent or total resistance?

Parallel Equations It = I1 + I2 + I3 + … So It/Vt = I1/Vt + I2/Vt + I3/Vt … But Vt = V1 = V2 = V3 =, implying It/Vt = I1/V1 + I2/V2 + I3/V3 … Or, by Ohm’s law, 1/Rt = 1/R1 + 1/R2 + 1/R3 + …

Parallel Circuit Rules VT = V1 = V2 = V3 = … IT = I1 + I2 + I3 + … 1/RT = 1/R1 + 1/R2 + 1/R3 + … Start here

Now map the current flow for circuit 2 Parallel Circuit: Follow the current Now map the current flow for circuit 2 IT A A R4 R5 R6 V2, I2 V3, I3 R1 V1, I1 R2 R3 A IT Circuit 1 Circuit 2

How does circuit 1 differ from circuit 2? Parallel Circuit: Follow the current How does circuit 1 differ from circuit 2? IT A A R4 R5 R6 V2, I2 V3, I3 R1 V1, I1 R2 R3 A IT

V V A R1 = 100 Ohms VT = 120V R2 = 200 Ohms V1 = V2 = VT RT = V2, I2 IT IT = I1 = I2 =

V V A R1 = 100 Ohms VT = 120V R2 = 200 Ohms V1 = R3 = 150 Ohms V2 = VT RT = V3 = V2, I2 V3, I3 V V R1 V1, I1 R2 R3 A IT IT = I1 = I2 = I3 =

V V A R1 = VT = 120V Rwire = 0.067 Ohms R2 = V1 = R3 = V2 = VT RT = V2, I2 V3, I3 V V R1 V1, I1 R2 R3 A IT IT = I1 = 5A I2 = 5A Find the equivalent resistance Req of this parallel network I3 = 5A

Parallel Circuit: Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit. VT V2, I2 V3, I3 R1 V1, I1 R2 R3 A IT

Parallel Circuit: Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit. Vt= V1= V2= V3= It = I1= I2= I3= Rt= R1= R2= R3= Pt= P1= P2= P3= VT V2, I2 V3, I3 R1 V1, I1 R2 R3 A IT

Parallel Circuit: Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2W, find the other values associated with this circuit. Vt=9 V1= 9 V2=9 V3=9 It =9.5 I1= 3 I2=1.97 I3= 4.5 Rt=0.95 R1=3 R2=4.6 R3=2 Pt=85.5 P1= 27 P2=18 P3=40.5 VT V2, I2 V3, I3 R1 V1, I1 R2 R3 A IT

Electrical Power & Ohm’s Law Volt = Joules / Coulomb Ampere = Coulomb / second Watt = Joule / Second Resistance = Kg m2/(Coulomb * sec2) Ooops!

Power Power is the rate of doing work (Watts) Power = Work / time Power = Volt * q / t but q/t = I Electrical Power = Voltage * Current = VI Electrical Energy = Power * Time = VIt

More Electric Energy Equations P = W/t Watt P = VI = V2/R =I2R Electric Energy (W)= Pt = VIt = V2/Rt =I2Rt Joules for all types of Energy

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

Monthly Service Charge is $18 Central Hudson Variable Costs $0.047 $0.002 -$0.007 $0.004 $0.001 $0.003 $0.065 $0.014 Total $0.134

per Kwh for all additional Kwhs Monthly Charges – (Includes the effect of Schedules 59, 91, & 93) $6.00 Basic Charge, plus $0.06850 per Kwh for the first 600 Kwhs $0.07933 per Kwh for the next 700 $0.09260 per Kwh for all additional Kwhs Example -   If you used 1450 Kwhs of electricity, your bill would be calculated like this: Basic Charge = x $41.100 $55.531 150 $13.890 Charge for $116.52 (franchise fees not included)

Calculate your electrical cost List appliances you use Estimate wattage Estimate usage Calculate cost

Homework: Chapter 23: Problems:page 488 1-6

Electrical Power & Ohm’s Law Volt = Joules / Coulomb Ampere = Coulomb / second Watt = Joule / Second Resistance = Ohms

More Power Problems P. 466: 19, 20, 21-25 Use the simplest form of the equation that matches the givens Check it with another form if desired

Practice Parallel Homework: Problems 8-14, ****16

Homework: Page: 465 Problems 1-7

Chap 22 Problems: 8-13, 15-20

Chapter 22 Problems: 21-25

Homework: Chapter 23: Problems:page 488 1-6 Discuss 7?

Homework: Chapter 23: Problems:page 488 1-6

Homework p. 526: 9, 10, 13

Homework Test Corrections p. 526: 9, 10, 13

Homework p. 465: 8, 10,11,12, 13, 16,17,18