ReviewAn 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 = I2R = V2/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

Material Resistivity

Aluminum 2.82 × 10–8

Copper 1.72 × 10–8

Gold 2.44 × 10–8

Nichrome 150. × 10–8

Silver 1.59 × 10–8

Tungsten 5.60 × 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.

R2

A

R1 +

V

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

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

R2

A

R1 +

V

Series Circuit Example

R3

A

V1, I1

+

IT

VV

VV

V3, I3

R1 VT

Given:

Vt = 10V

R1 = 5

I2 = 1A

P3 = 2W

R2 VV V2, I2

Vt = 10V V1 = V2 = V3 =

It = I1 = I2 = 1A I3 =

Rt = R1 = 5 R2 = R3 =

Pt = P1 = P2 = P3 = 2W

Series Circuit Example

R3

A

V1, I1

+

IT

VV

VV

V3, I3

R1 VT

Given:

Vt = 10V

R1 = 5

I2 = 1A

P3 = 2W

R2 VV V2, I2

Vt = 10V V1 = 5V V2 = 3V V3 = 2V

It = 1A I1 = 1A I2 = 1A I3 = 1A

Rt = 10 R1 = 5 R2 = 3 R3 = 2

Pt = 10W P1 = 5W P2 = 3W P3 = 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

R3 V2

A

VV

IT

R1

IT

R2 VVVV V3V1

Parallel Circuit: •Voltmeters 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

I1

I2 + I3

IT

IT = I1 + I2 + I3 by Conservation of charge (conservation of matter)

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 Equations

AIT

R1

IT

R2

Parallel Circuit: •Follow the current•If R1 > R2 > R3, what will the relationship between I1, I2, and I3 be? V1, V2, V3?

V1, I1V3, I3

V2, I2

R3

Circuit 1

AIT

R1

VT

R2

Parallel Circuit: •Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2, find the other values associated with this circuit.

V3, I3

V2, I2

R3 V1, I1

Vt = V1 = V2 = V3 =

It = I1 = 3A I2 = I3 =

Rt = R1 = 3 R2 = R3 = 2

Pt = P1 = P2 = 18W P3 =

AIT

R1

VT

R2

Parallel Circuit: •Given I1 = 3A, R1= 3A, P2 = 18W, and R3 = 2, find the other values associated with this circuit.

V3, I3

V2, I2

R3 V1, I1

Vt =9V V1 = 9V V2 =9V V3 =9V

It =9.5A I1 = 3A I2 =2A I3 =4.5A

Rt =0.95 R1 = 3 R2 =4.5 R3 = 2

Pt =85.5W P1 = 27W P2 = 18W P3 = 40.5W

Series Circuit Example: Voltage Divider

A

V1, I1+

IT

VVR1 VT

Given:

Vt = 24V

Choose values of R1 and R2 to

produce 20V across R2

R2 VVV2, I2

Vt =24V V1 =4 V2 =20

It = I1 = I2 =

Rt = R1 = R2 =

Pt = P1 = P2 =

Series Circuit Example: Voltage Divider

A

V1, I1+

IT

VVR1 VT

Given:

Vt = 24V

Choose values of R1 and R2 to

produce 20V across R2

R2 VVV2, I2

Vt =24V V1 =4 V2 =20

It = 1A I1 = 1A I2 = 1A

Rt = 24 R1 = 4 R2 =20

Pt =24W P1 = 4W P2 = 20W

AIT

R1

VT

R2

Series / Parallel Circuit: •Given V4=12, I1 = 3A, R2= 2, R3=3, P3 = 18W. Find the other values.

V3, I3

V2, I2

R3

V4, I4

V1, I1

R4

Vt = V1 = V2 = V3 = V4 =12V

It = I1 = 3A I2 = I3 = I4 =

Rt = R1 = R2 =2 R3 =3 R4 =

Pt = P1 = P2 = P3 = 18W P4=

AIT

R1

VT

R2

Series / Parallel Circuit: •Given V4=12, I1 = 3A, R2= 2, R3=3, P3 = 18W. Find the other values.

V3, I3

V2, I2

R3

V4, I4

V1, I1

R4

Vt =19.34V V1 =7.34V V2 =7.34V V3 =7.34V V4 =12V

It =9.12A I1 = 3A I2 =3.67A I3 =2.45 I4 =9.12A

Rt =2.12 R1 = 2.45 R2 =2 R3 =3 R4 = 1.31

Pt =176.4W P1 =22W P2 =26.94W P3 = 18W P4=109.4W