Review An electric circuit is composed of what 3 elements? Conductor, potential difference, closed loop What are the units of voltage? Joules / Coulomb Electric potential energy / unit charge Current? Amperes / second A flow of charged particles Resistance? Ohms

Current Electric current is the rate of flow of charge I = Δq/ Δt Ampere = Coulomb per second (passing by a point in a circuit)

Ohm’s Law: Ohm's Law …says that, for many materials under a wide range of conditions, the voltage, V, and current, I, are linearly related, which implies resistance, R, is independent of V and I.

Ohm’s Law Mnemonic

Ohm’s Law: Ohm's Law …says that, for many materials under a wide range of conditions, the voltage, V, and current, I, are linearly related, which implies resistance, R, is independent of V and I. When does it not apply? (Most important case)  Changing Temperature

Questions What is the effect on the current through a system if the voltage is doubled? Resistance doubled? Both? A device connected to a 1.5V battery conducts a drives a 45x10 -6 A current, while the same device connected to a 3V battery conducts a 90x10 -3 A current. Is the device ohmic?

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 = IV * t

Electrical Power P= IV “Poison Ivy”

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

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

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

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

Diagramming circuits

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. R2R2 A A R1R1 + V

Series Circuit Current : One path for the flow of charge I t =I 1 =I 2 =I 3 Resistance must increase because length increases R t -=R 1 +R 2 +R 3 Voltage must add to Zero V t -V 1 -V 2 -V 3 =0 V t =V 1 +V 2 +V 3

Series and Parallel Circuits What does it mean to go in series? –Single file What does it mean to go in parallel? –Multiple paths

Series Circuit: –ammeters are always in the circuit, they measure flow of charge Ammeters should always have low resistance –Otherwise they will affect the measurement by adding resistance R2R2 A A R1R1 + V

Series Circuit Example R3R3 A A V 1, I 1 + ITIT VV VV V 3, I 3 R1R1 VTVT Given: V t = 10V R 1 = 5  I 2 = 1 A P 3 = 2W R2R2 VV V 2, I 2 Vt = 10VV1 =V2 =V3 = It =I1 =I2 = 1AI3 = Rt = R1 = 5  R2 =R3 = Pt =P1 =P2 =P3 = 2W

Series Circuit Example R3R3 A A V 1, I 1 + ITIT VV VV V 3, I 3 R1R1 VTVT Given: V t = 10V R 1 = 5  I 2 = 1 A P 3 = 2W R2R2 VV V 2, I 2 Vt = 10VV1 = 5VV2 = 3VV3 = 2V It = 1AI1 = 1AI2 = 1AI3 = 1A Rt = 10  R1 = 5  R2 = 3  R3 = 2  Pt = 10WP1 = 5WP2 = 3WP3 = 2W

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

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 charges have the same drop

R3R3 V2V2 A VV ITIT R1R1 A ITIT R2R2 VVVV V3V3 V1V1 Parallel Circuit: V oltmeters are parallel to the circuit, they measure the potential Voltmeters should always have high resistance Otherwise they will allow current to flow through them and reduce effective resistance I1I1 I 2 + I 3 ITIT I T = I 1 + I 2 + I 3 by Conservation of charge (conservation of matter)

Parallel Equations I t = I 1 + I 2 + I 3 + … So I t /V t = I 1 /V t + I 2 /V t + I 3 /V t … But V t = V 1 = V 2 = V 3 =, implying I t /V t = I 1 /V 1 + I 2 /V 2 + I 3 /V 3 … Or, by Ohm’s law, 1/R t = 1/R 1 + 1/R 2 + 1/R 3 + …

Parallel Equations

A ITIT R1R1 ITIT R2R2 Parallel Circuit: Follow the current If R1 > R2 > R3, what will the relationship between I1, I2, and I3 be? V1, V2, V3? V 1, I 1 V 3, I 3 V 2, I 2 R3R3 A Circuit 1

A ITIT R1R1 VTVT R2R2 Parallel Circuit: Given I 1 = 3A, R 1 = 3A, P 2 = 18W, and R 3 = 2 , find the other values associated with this circuit. V 3, I 3 V 2, I 2 R3R3 V 1, I 1 Vt =V1 =V2 =V3 = It =I1 = 3AI2 =I3 = Rt = R1 = 3  R2 = R3 = 2  Pt =P1 =P2 = 18WP3 =

A ITIT R1R1 VTVT R2R2 Parallel Circuit: Given I 1 = 3A, R 1 = 3A, P 2 = 18W, and R 3 = 2 , find the other values associated with this circuit. V 3, I 3 V 2, I 2 R3R3 V 1, I 1 Vt =9VV1 = 9VV2 =9VV3 =9V It =9.5AI1 = 3AI2 =2AI3 =4.5A Rt =0.95  R1 = 3  R2 =4.5  R3 = 2  Pt =85.5WP1 = 27WP2 = 18WP3 = 40.5W

Series Circuit Example: Voltage Divider A A V 1, I 1 + ITIT VV R1R1 VTVT Given: V t = 24 V Choose values of R 1 and R 2 to produce 20V across R 2 R2R2 VV V 2, I 2 Vt =24VV1 =4V2 =20 It =I1 =I2 = Rt =R1 =R2 = Pt =P1 =P2 =

Series Circuit Example: Voltage Divider A A V 1, I 1 + ITIT VV R1R1 VTVT Given: V t = 24 V Choose values of R 1 and R 2 to produce 20V across R 2 R2R2 VV V 2, I 2 Vt =24VV1 =4V2 =20 It = 1AI1 = 1AI2 = 1A Rt = 24  R1 = 4  R2 =20  Pt =24WP1 = 4WP2 = 20W

A ITIT R1R1 VTVT R2R2 Series / Parallel Circuit: Given V 4 =12, I 1 = 3A, R 2 = 2, R 3 =3, P 3 = 18W. Find the other values. V 3, I 3 V 2, I 2 R3R3 V 4, I 4 V 1, I 1 R4R4 Vt =V1 =V2 =V3 =V4 =12V It =I1 = 3AI2 =I3 =I4 = Rt =R1 = R2 =2  R3 =3  R4 = Pt =P1 =P2 =P3 = 18WP4=

A ITIT R1R1 VTVT R2R2 Series / Parallel Circuit: Given V 4 =12, I 1 = 3A, R 2 = 2, R 3 =3, P 3 = 18W. Find the other values. V 3, I 3 V 2, I 2 R3R3 V 4, I 4 V 1, I 1 R4R4 Vt =19.34VV1 =7.34VV2 =7.34VV3 =7.34VV4 =12V It =9.12AI1 = 3AI2 =3.67A I3 =2.45  I4 =9.12A Rt =2.12  R1 = 2.45  R2 =2  R3 =3  R4 = 1.31  Pt =176.4WP1 =22WP2 =26.94WP3 = 18WP4=109.4W