Current Electricity and Circuits

1
Current Electricityand Circuits
V
R

• Chapter 22 and 23

I
I Q/t
2
Electric Circuits

• Now that we have the concept of voltage, we can
  use this concept to understand electric circuits
• Just like we can use pipes to carry water, we can
  use wires to carry electricity.
• The flow of water through pipes is caused by
  pressure differences, and the flow is measured by
  volume of water per time

V Electrical pressure - measured in volts.
3
Electric Current

• In electricity, the concept of voltage will be
  like pressure. Water flows from high pressure to
  low pressure electricity flows from high
  voltage to low voltage.
• But what flows in electricity? Charges!
• How do we measure this flow? Current
• I DQ/Dt
• Electric current is measured in Amperes, in honor
  of Andre Marie Ampere.

1 Amp 1 Coulomb per 1 second 1 C/s
4
Direction of Current Flow

• For historical reasons, current is conventionally
  thought to flow from the positive to the negative
  potential in a circuit.
• Current flow is the rate of flow of positive
  charge (Its really the electrons flowing in the
  opposite direction)
• Electron flow is from a lower potential (voltage)
  to a higher potential (voltage).
• Electrons carry negative charge
• Positive current flow is in opposite direction

5
Conventional Current

• Conventional current flows from high V to low V
  and to across components like resistors.
• Conventional current flows from the positive side
  of the battery to the around to the negative
  side. Dont be confused by diagrams that look
  like it is flowing across the battery from the
  negative to the positive.

I
I
-
- high V
low V R1 R2
6
Power, Current and Voltage
P W/t
Power work/time
For electric circuits,
P V .I
Power electric potential difference . current
because,
(work/charge).(charge/time)
Charge divides out leaving W/t, which is power
Electrical energy is a measure of the amount of
power used and the time of use. Electrical
energy, kilowatt hours, is the product of the
power and the time.
7
Battery or Cell Voltage Source

• A battery in an electrical circuit plays the same
  role as a pump in a water system.
• Because of the pumping nature of voltage
  sources, we need to have a complete circuit
  before we have a current.
• Just like a pump needs water coming into it in
  order to pump water out, so the voltage source
  needs charges coming into it (into the negative
  terminal) in order to pump them out (of the
  positive terminal).

Does the battery or power supply actually supply
the charges that will flow through the circuit?
8
Voltage Sources
9
Symbols for Voltage Sources

• In circuit diagrams, symbols are used to
  represent each component. The following symbols
  may be used for voltage sources

Note The battery will be the voltage source used
in our diagrams
10
Ground

• Ground refers to the reference terminal to
  which all other voltages are measured.
• The earth is really just one big ground node.
• Most people choose the earth as the reference
  ground when a connection to it is available.

11
Ground Symbol
12
Simple Circuit

• A simple circuit contains the minimum things
  needed to have a functioning electric circuit. A
  simple circuit requires three (3) things
• A source of electrical potential difference or
  voltage. (typically a battery or electrical
  outlet)
• A conductive path which would allow for the
  movement of charges. (typically made of wire)
• An electrical resistance (resistor) which is
  loosely defined as any object that uses
  electricity to do work. (a light bulb, electric
  motor, heating element, speaker, etc.)

13
Ohms Law

• It takes pressure to make fluid flow due to the
  viscosity of the fluid and the size of the pipe.
• Voltage is required to make electric current flow
  due to the resistance in the circuit.
• By experiment we find that if we increase the
  voltage, we increase the current V is
  proportional to I. The constant of
  proportionality we call the. resistance, R

14
Ohms Law
The ratio of potential difference to current is
constant.

• If R V/I is a constant value for a given
  resistor, then that resistor is said to obey
  Ohms Law.
• Ohms Law in equation form VIR
• The SI unit of resistance is the Ohm, W, named in
  honor of Georg Simon Ohm.

15
Ohms Law
16
Resistance

• The resistance depends on material and geometry
  (shape).
• For a wire R r L / A where where r is called
  the resistivity (in Ohm-m) and measures how hard
  it is for current to flow through the material, L
  is the length of the wire, and A is the
  cross-sectional area of the wire.
• In a circuit the symbol used for resistors is
  usually
• In circuits, the resistance of resistors is often
  given or can be calculated. The resistance of the
  wire connecting the circuit is sometimes
  neglected.

17
Resistance and Temperature

• Many circuit elements do not obey Ohms Law.
• Resistors that get hot, like light bulbs and
  heating elements, do not keep a constant
  resistance. Resistance generally increases as
  objects become hotter.

18
Series and Parallel Circuits

• There are two ways devices can be connected in a
  circuit, series or parallel.
• Current flows differently through each type of
  circuit so each requires a different set of
  equations.

R1
I
V1
R2

Vbat
V2
Itotal
-

Resistors connected in series
R1
I1
Vbat
R2
I2
-
Resistors connected in parallel
19
Series Resistors - Equations
Current is constant There is only one path for
the current to take so in a series circuit,
resistance and voltage add, but current stays the
same.
1. total resistance is the sum of the
separate resistors
RT R1 R2 R3 ...
2. current is the same through each resistor
IT I1 I2 I3 ...
3. total potential difference is the sum of each
VT V1 V2 V3 ...
20
Parallel Resistors - Equations

• In a parallel circuit, resistance adds as
  reciprocals, voltage stays the same, and current
  splits

1. reciprocal of the total resistance is the sum
of the reciprocals of the separate resistors
1/RT 1/R1 1/R2 1/R3 ...
2. total current is the sum of the current
through each resistor
IT I1 I2 I3 ...
3. potential difference is the same across
each resistor
VT V1 V2 V3 ...
21
Kirchhoffs Current Law Junction Rule

• Kirchhoffs current law says Current into
  junction Current leaving junction OR The sum of
  all the currents entering a node is zero

I1 I2 I3 OR I1 I2 I3 0
node
Io
How much is the current Io , if I2 is 2.5 mA and
I3 is 4 mA?
22
Kirchhoffs Current Law applies to all types of
networks
Fiber optic network (I is light intensity)
I1
I2
KCL for light
I1 I2 I3
I3
23
Kirchhoffs Current Law applies to all types of
networks
Human Blood Vessels (f is blood flow rate)
f2
f1
f1
KCL for blood flow
f1 f2 f3
f3
24
Kirchhoffs Voltage Law Loop Rule

• Kirchhoffs Voltage Law Sum of all voltage drops
  and voltage rises in a circuit (a closed loop)
  equals zero OR The voltage measured between any
  two nodes does not depend of the path taken.

V1 V2 V3
V1 V2 V4
V3 V4
25
Kirchhoffs Voltage Law Loop Rule
Kirchhoffs Voltage Law V1 V2 V3
OR
V1 V2 V3 0
26
Using the Loop Rule

• Assign symbols and directions of currents in the
  loop
• If the direction is chosen wrong, the current
  will come out with a right magnitude, but a
  negative sign (its ok).
• Choose a direction (cw or ccw) for going around
  the loop. Record drops and rises of voltage
  according to this
• If a resistor is traversed in the direction of
  the current -V -IR
• If a resistor is traversed in the direction
  opposite to the current VIR
• If EMF is traversed from to E
• If EMF is traversed from to -E

27
Using the Loop Rule

• Loops can be chosen arbitrarily. For example, the
  circuit below contains a number of closed paths.
  Three have been selected for discussion.

Suppose that for each element, respective current
flows from to - signs.
-


-
v2
v5
Path 1
-
-
-
v1
v4
v6



Path 2
v3
v7


-
-
Path 3
-


v8
v12
v10

-
-

-
-
v11
v9

28
Using the Loop Rule
b
Using sum of the drops 0

-


-
v2
v5
-
-
-
Blue path, starting at a - v7 v10 v9 v8
0
v1
v4
v6



v3
v7


-
-
a

Red path, starting at b v2 v5 v6 v8
v9 v11 v12 v1 0
-


v8
v12
v10

-
-
Yellow path, starting at b v2 v5 v6 v7
v10 v11 - v12 v1 0

-
-
v11
v9

29
Using the Loop Rule

• Example For the circuit below find I, V1, V2,
  V3, V4 and the power supplied by the 10 volt
  source.

1. For convenience, we start at point a and sum
   voltage drops 0 in the direction of the current
   I.

2. We note that V1 - 20I, V2 40I, V3
- 15I, V4 5I (2)
3. We substitute the above into Eq. 1 to obtain
Eq. 3 below.
10 20I 30 15I 5I 20 40I 0
(3)
Solving this equation gives, I 0.5 A.
30
Using the Loop Rule
Using this value of I in Eq. 2 gives
V1 - 10 V
V3 - 7.5 V
V2 20 V
V4 2.5 V
P10(supplied) -10I - 5 W
(We use the minus sign in 10I because the
current is entering the terminal) In this case,
power is being absorbed by the 10 volt supply.
31
P, W
V, V
R, W
I, A
E 12 V
8.0
R1
2.0
R1
R3
R2
5.0
R3
RT
R2
VT
IT
PT
32
P, W
V, V
R, W
I, A
E 12 V
8.0
R1
0.80
6.4
5.1
2.0
0.80
1.6
1.3
R1
R3
R2
5.0
0.80
4.0
3.2
R3
RT 15 ?
R2
VT 12 V
IT 0.80 A
PT 9.6 W
33
P, W
R, W
V, V
I, A
E 12 V
12
R1
8.0
R2
R1
12
R3
R2
RT
R3
VT
IT
PT
34
P, W
R, W
V, V
I, A
E 12 V
12
12
1.0
12
R1
1.5
8.0
12
18
R2
R1
12
1.0
12
12
R3
R2
RT 3.42 ?
R3
VT 12 V
IT 3.50 A
PT 42 W
35
Toll Road Circuit Analogy
Adding toll booths in series increases resistance
and slows the current flow. Adding toll booths
in parallel lowers resistance and increases the
current flow.
36
Combined Series parallel circuits

• Rt R1 1/(1/R2 1/R3) add R2 and R3 as
  parallel then add the result to R1
• Vt V1 (V2 V3)
• It I1 I2 I3 total current goes through R1
  but splits when it go through R2 and R3

37
Internal Resistance
Real batteries are constructed from materials
which possess non-zero resistance. It follows
that real batteries are not just pure voltage
sources. They also possess internal resistances.
A battery can be modeled as an emf connected in
series with a resistor , which represents its
internal resistance.
38
Capacitor /Water Tower

• A water tower holds water. A capacitor holds
  charge.
• While we normally define the capacity of a water
  tank by the TOTAL AMOUNT of water it can hold, we
  define the capacitance of an electric capacitor
  as the AMOUNT OF CHARGE PER VOLT instead. C Q/V
• There is a TOTAL AMOUNT of charge a capacitor can
  hold, and this corresponds to a MAXIMUM VOLTAGE
  that can be placed across the capacitor. Each
  capacitor DOES HAVE A MAXIMUM VOLTAGE.
• If an electric capacitor is over-filled or
  equivalently a higher voltage is placed across
  the capacitor than the listed maximum voltage It
  will break by having the charge escape. This
  escaping charge is like lightning - a spark that
  usually destroys the capacitor

39
Capacitors In Series

• There is only one way around the circuit, and you
  have to jump BOTH capacitors in making the
  circuit
• The positive charge on the left plate of C1 will
  attract a negative charge on the right plate, and
  the negative charge on the bottom plate of C2
  will attract a positive charge on the top plate -
  just what is needed to give the negative charge
  on the right plate of C1.

C1
(Q1 ? )

Q1 -Q 1
Q2
V
C2
-Q2
( ? Qtotal)
Vtotal (V1 V2)
1/C1 1/C2 1/Ceffective
Qtotal Q1 Q2
40
Capacitors Parallel

• For parallel, both plates are across the same
  voltage, so Vtotal V1 V2 . The charge can
  accumulate on either plate, so Qtotal (Q1
  Q2).
• Since the Qs are in the numerator, we have
  Ceff C1 C2.

Q1
Q2
C1
C2
V
-Q1
-Q2
Q1 ?
? Qtotal (Q1Q2)
? Q2
41
The Light Bulb and its Components

• Has two metal contacts at the base which connect
  to the ends of an electrical circuit
• The metal contacts are attached to two stiff
  wires, which are attached to a thin metal
  filament.
• The filament is in the middle of the bulb, held
  up by a glass mount.
• The wires and the filament are housed in a glass
  bulb, which is filled with an inert gas, such as
  argon.

42
Light bulbs and Power

• Power dissipated by a bulb relates to the
  brightness of the bulb. The higher the power,
  the brighter the bulb.
• Power is measured in Watts W
• Power, P IV, can also be written P I2R or P
  V2 / R by using Ohms law and doing some
  substitutions.
• If we wanted a higher power light bulb, should we
  have a bigger resistance or a smaller resistance
  for the light bulb?

43
Light bulbs and Power - Answer

• Answer In this case, the voltage is being held
  constant due to the nature of the batteries.
  This means that the current will change as we
  change the resistance. Thus, the P V2 / R
  would be the most straight-forward equation to
  use. This means that as R goes down, P goes up.
  (If we had used the P I2R formula, as R goes
  up, I would decrease so it would not be clear
  what happened to power.)
• The answer for more power, lower the
  resistance. This will allow more current to flow
  at the same voltage, and hence allow more power!

44
Light bulbs and Power

• The three light bulbs in the circuit all have the
  same resistance. Given that brightness is
  proportional to power dissipated, the brightness
  of bulbs B and C together, compared with the
  brightness of bulb A, is
• 1. twice as much.
• 2. the same.
• 3. half as much.

45
RC circuits

• When switch is closed, current flows because
  capacitor is charging
• As capacitor becomes charged, the current slows
  because the voltage across the resistor is ? - Vc
  and Vc gradually approaches ?.
• Once capacitor is charged the current is zero

q
q
Charge across capacitor
RC is called the time constant
46
RC circuits

• If a capacitor is charged and the switch is
  closed, then current flows and the voltage on the
  capacitor gradually decreases.
• This leads to decreasing charge

q
Charge across capacitor
0.37q
47
Sources

• www.physics.ubc.ca/outreach/phys420/p420_04/mitsuk
  o/OhmsLaw-Gr10-Science.ppt
• http//physics.bu.edu/duffy/PY106
• Physics by Zitzewitz
• www.glenbrook.k12.il.us/GBSSCI/PHYS/Class
• www.cbu.edu/jholmes/P202/P1elec2.ppt