Current

1
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

2
Current

• Electric current is the rate of flow of charge
• I ?q/ ?t
• Ampere Coulomb per second (passing by a point
  in a circuit)

3
Ohms 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.
4
Ohms Law Mnemonic
5
Ohms 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

6
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?

7
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

8
Electrical Power

• P IV Poison Ivy

9
Electrical Power

• P IV I2R V2/R

10
Electrical Power

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

11
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)

12
Low resistance

• Short
• Fat
• cold

13
High Resistance

• Long
• Thin
• Hot

14
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
15
Diagramming circuits
16
Kirchoffs Junction Rule

• Conservation of charge

17
Kirchoffs Loop Rule

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

V

R1
R2
18
Series Circuit

• Current One path for the flow of charge
• ItI1I2I3
• Resistance must increase because length increases
• Rt-R1R2R3
• Voltage must add to Zero
• Vt-V1-V2-V30 VtV1V2V3

19
Series and Parallel Circuits

• What does it mean to go in series?
• Single file
• What does it mean to go in parallel?
• Multiple paths

20

• 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

V

R1
R2
21

• Series Circuit Example

IT
Vt 10V V1 V2 V3
It I1 I2 1A I3
Rt R1 5W R2 R3
Pt P1 P2 P3 2W

VT
V
V
V1, I1
R1
V2, I2
V
V
R2
V
V
R3
V3, I3
Given Vt 10V R1 5W I2 1A P3 2W
22

• Series Circuit Example

IT
Vt 10V V1 5V V2 3V V3 2V
It 1A I1 1A I2 1A I3 1A
Rt 10W R1 5W R2 3W R3 2W
Pt 10W P1 5W P2 3W P3 2W

VT
V
V
V1, I1
R1
V2, I2
V
V
R2
V
V
R3
V3, I3
Given Vt 10V R1 5W I2 1A P3 2W
23
Series and Parallel Circuits
L
Series Single Path, high effective resistance
a
L
A
Parallel Multiple Paths, low effective
resistance
24
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

25

• 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

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
26
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 Ohms law,
• 1/Rt 1/R1 1/R2 1/R3

27
Parallel Equations
28

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

IT
V2, I2
V3, I3
R1
R2
V1, I1
R3
IT
Circuit 1
29

• 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 3A I2 I3
Rt R1 3W R2 R3 2W
Pt P1 P2 18W P3
VT
V2, I2
V3, I3
R3
V1, I1
R1
R2
IT
30

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

Vt 9V V1 9V V2 9V V3 9V
It 9.5A I1 3A I2 2A I3 4.5A
Rt 0.95W R1 3W R2 4.5W R3 2W
Pt 85.5W P1 27W P2 18W P3 40.5W
VT
V2, I2
V3, I3
R3
V1, I1
R1
R2
IT
31

• Series Circuit Example Voltage Divider

Vt 24V V1 4 V2 20
It I1 I2
Rt R1 R2
Pt P1 P2
IT
Given Vt 24V Choose values of R1 and R2 to
produce 20V across R2

VT
V1, I1
V
V
R1
V2, I2
V
V
R2
32

• Series Circuit Example Voltage Divider

Vt 24V V1 4 V2 20
It 1A I1 1A I2 1A
Rt 24W R1 4W R2 20W
Pt 24W P1 4W P2 20W
IT
Given Vt 24V Choose values of R1 and R2 to
produce 20V across R2

VT
V1, I1
V
V
R1
V2, I2
V
V
R2
33

• Series / Parallel Circuit
• Given V412, I1 3A, R2 2, R33, P3 18W.
  Find the other values.

Vt V1 V2 V3 V4 12V
It I1 3A I2 I3 I4
Rt R1 R2 2W R3 3W R4
Pt P1 P2 P3 18W P4
V4, I4
R4
VT
V2, I2
V3, I3
R3
V1, I1
R1
R2
IT
34

• Series / Parallel Circuit
• Given V412, I1 3A, R2 2, R33, P3 18W.
  Find the other values.

Vt 19.34V V1 7.34V V2 7.34V V3 7.34V V4 12V
It 9.12A I1 3A I2 3.67A I3 2.45A I4 9.12A
Rt 2.12W R1 2.45W R2 2W R3 3W R4 1.31W
Pt 176.4W P1 22W P2 26.94W P3 18W P4109.4W
V4, I4
R4
VT
V2, I2
V3, I3
R3
V1, I1
R1
R2
IT