Electric Circuits
Electric potential difference
Electromotive force- emf
Circuits
Conductors and resistors
Resistivity and Resistance
Circuit Diagrams
Electric Current & DC Circuits
Measurement
1. Electric Potential Difference
1). Electric Potential Energy
WAB  mghA  mghB  GPE A  GPE B
1). Potential Energy
In electric field:
1). electric Potential Energy
WAB  EPE A  EPE B
When E is uniform:
WAB  q0 E (d A  d B )
WAB EPE A EPE B


qo
qo
qo
The potential energy per unit charge
is called the electric potential.
And :
WAB EPE A EPE B


 VA  VB
qo
qo
qo
Electric Potential Difference is:
(q0 E (d A  d B ))
V 
 Ed A  Ed B
q0
SI Unit of Electric Potential: joule/coulomb = volt (V)
2). The Electric Potential Difference
The Accelerations of Positive and Negative Charges
A positive test charge is released from A and accelerates towards B. Upon
reaching B, the test charge continues to accelerate toward C. Assuming that
only motion along the line is possible, what will a negative test charge do when
released from rest at B?
A positive charge accelerates from a region of higher electric potential
toward a region of lower electric potential.
A negative charge accelerates from a region of lower potential toward
a region of higher potential.
The Electric Field and Potential Are Related
2. Electromotive Force – emf
emf – is the voltage developed by any source of
electrical energy such as a battery or dynamo. It is
generally defined as the potential for a source in a
circuit.
measured in volts
2. Electromotive Force from Electric batteryVoltage
Various cells and batteries (top-left to bottomright): two AA, one D, one handheld ham
radiobattery, two 9-volt (PP3), two AAA, one C,
onecamcorder battery, one cordless
phone battery.
The symbol for a battery in a circuit diagram. It
originated as a schematic drawing of the earliest
type of battery, a voltaic pile.
Line art drawing of a dry cell:
1. brass cap, 2. plastic seal, 3. expansion space,
4. porous cardboard, 5. zinc can, 6. carbon rod,
7. chemical mixture.
The SI unit on electric potential difference is the
volt, V (in honor of Alessandro Volta).
Within the electrochemical cells of the battery, there is an
electric field established between the two terminals, directed
from the positive terminal towards the negative terminal.
The negative terminal is described as the low potential
terminal.
How battery works:
In a battery-powered electric circuit, the chemical
energy is used to do work.
Chemical energy is transformed into electric
potential energy within the internal circuit (i.e.,
the battery).
Once at the high potential terminal, a positive
test charge will then move through the external
circuit and do work upon the light bulb or the
motor or the heater coils.
The positive test charge returns to the negative
terminal at a low energy and low potential, ready
to repeat the cycle (or should we say circuit) all
over again.
3. Circuits
An electric circuit is an external path
that charges can follow between two
terminals using a conducting
material.
1). Requirements
•
the path must be complete and
unbroken--There must be a closed
conducting loop in the external
circuit that stretches from the high
potential, positive terminal to the
low potential, negative terminal.
•
The Requirement of an Energy
Supply--There must be an energy
supply capable doing work on
charge to move it from a low
energy location to a high energy
location and thus establish an
electric potential difference across
the two ends of the external circuit.
Electromotive Force and Current
In an electric circuit, an energy source and an energy consuming device
are connected by conducting wires through which electric charges move.
2). Symbols for circuit elements
A Ideal conductor - generally
assume that that R=0
Ideal EMF NOTE – device is
asymmetric
Ideal Resistor
EMF with internal resistance
Ideal Voltmeter - generally
assume that that R=∞ - No
current flows through an ideal
voltmeter –
Ideal Ammeter - generally
assume that that R=0
Electrically, an ideal ammeter is
a perfect conductor
Electromotive Force and Current
Within a battery, a chemical reaction occurs that transfers electrons from
one terminal to another terminal.
The maximum potential difference across the terminals is called the
electromotive force (emf).
emf give circuit voltage supply which is represented by V
3). Electric Current
The electric current is the amount of charge per unit time that passes
through a surface that is perpendicular to the motion of the charges.
q
I
t
One coulomb per second equals one ampere (A).
Current, resistance and electromotive force
Current
Current is a concept with wide spread applications describing the rate of flow of
some quantity that can be:
-Throughput of cars per time interval:
-water volume coming out of a hose per time interval:
20.1 Electromotive Force and Current
If the charges move around the circuit in the same direction at all times,
the current is said to be direct current (dc).
If the charges move first one way and then the opposite way, the current is
said to be alternating current (ac).
20.1 Electromotive Force and Current
Example 1 A Pocket Calculator
The current in a 3.0 V battery of a pocket calculator is 0.17 mA. In one hour
of operation, (a) how much charge flows in the circuit and (b) how much energy
does the battery deliver to the calculator circuit?
(a)
(b)


q  I t   0.17 103 A 3600 s   0.61 C
Energy  Charge 
Energy
 0.61 C3.0 V   1.8 J
Charge
20.1 Electromotive Force and Current
Conventional current is the hypothetical flow of positive charges that would
have the same effect in the circuit as the movement of negative charges that
actually does occur.
Electron's journey through a circuit
In the wires of electric circuits,
an electron is the actual charge
carrier.
zigzag path that results from
countless collisions with the
atoms of the conducting wire
Conductor’s Resistance
Some conductors "conduct" better or worse than others.
Reminder:
conducting means a material allows for the free flow of
electrons.
The flow of electrons is just another name for current.
Another way to look at it is that some conductors resist
current to a greater or lesser extent.
We call this resistance, R. Resistance is measured in
ohms which is noted by the Greek symbol omega (Ω)
Demo
http://phet.colorado.edu/en/simulations/category/physics/electricity-magnetsand-circuits
Battery - resistor circuit
Circuit Construction Kit (DC Only)
Eg1.
12 C of charge passes a location in a circuit in 10
seconds. What is the current flowing past the point?
Eg2.
A circuit has 10 A of current.H ow long does it take
20C of charge to travel through the circuit?
Eg3.
20 C of charge passes a location in a circuit in 30
seconds. What is the current flowing past the point?
eg4.
A circuit has 10 A of current. How much charge
travels through the circuit after 20s?
Eg5.
A circuit has 3 A of current. How long does it take
45 C of charge to travel through the circuit?
eg6
A circuit has 2.5 A of current. How much charge
travels through the circuit after 4s?
Basic Circuits
• The circuit cannot have gaps.
• The bulb had to be between the wire
and the terminal.
• A voltage difference is needed to make
the bulb light.
• The bulb still lights regardless of which
side of the
• battery you place it on.
4. Ohm’s Law
The resistance (R) is defined as the
ratio of the voltage V applied across
a piece of material to the current I through
the material.
4. Ohm’s Law
OHM’S LAW
The ratio V/I is a constant, where V is the
voltage applied across a piece of material
and I is the current through the material:
V
 R  constant
I
or
V  IR
SI Unit of Resistance: volt/ampere (V/A) = ohm (Ω)
4 Ohm’s Law
To the extent that a wire or an electrical
device offers resistance to electrical flow,
it is called a resistor.
4 Ohm’s Law
Example 1 A Flashlight
The filament in a light bulb is a resistor in the form
of a thin piece of wire. The wire becomes hot enough
to emit light because of the current in it. The flashlight
uses two 1.5-V batteries to provide a current of
0.40 A in the filament. Determine the resistance of
the glowing filament.
V
3.0 V
R 
 7.5 
I 0.40 A
2.
A flashlight has a resistance of 30 Ω and is
connected by a wire to a 90 V source of voltage.
What is the current in the flashlight?
3.
What is the current in a wire whose resistance is
3 Ω if 1.5 V is applied to it?
5.
How much voltage is needed in order to produce
a 0.70 A current through a 490 Ω resistor?
6.
How much voltage is needed in order to produce
a 0.5 A current through a 150 Ω resistor?
7.
What is the resistance of a rheostat coil, if 0.05 A of
current flows through it when 6 V is applied across it?
8.
What is the resistance of a rheostat coil, if 20 A of
current flows through it when 1000 V is applied
across it?
5 Resistance and Resistivity
For a wide range of materials, the resistance of a piece of
material of length L and cross-sectional area A is
L
R
A
resistivity in units of ohm·meter
the measure of a conductor's resistance to conduct is called its
resistivity.
Each material has a different resistivity.
Resistivity is abbreviated using the Greek letter rho (ρ).
Combining what we know about A, L, and ρ, we can find a
conductor's total resistance.
Resistance, R, is measured in Ohms (Ω). Ω is the
Greek letter Omega.
Cross-sectional area, A, is measured in m2
Length, L, is measured in m
Resistivity, ρ, is measured in Ωm
5 Resistance and Resistivity
L
R
A
What is the resistance of a
good conductor?
Low; low resistance means
that electric charges are free
to move in a conductor.
Check:
Rank the following materials in order of best
conductor to worst conductor.
A Iron, Copper, Platinum
B Platinum, Iron, Copper
C Copper, Iron, Platinum
5 Resistance and Resistivity
Example 3 Longer Extension Cords
The instructions for an electric lawn mower suggest that a 20-gauge extension
cord can be used for distances up to 35 m, but a thicker 16-gauge cord should
be used for longer distances. The cross sectional area of a 20-gauge wire is
5.2x10-7Ω·m, while that of a 16-gauge wire is 13x10-7Ω·m. Determine the
resistance of (a) 35 m of 20-gauge copper wire and (b) 75 m of 16-gauge
copper wire.
(a)
(b)


L 1.72 108   m 35 m 
R 
 1.2 
-7
2
A
5.2 10 m


L 1.72 10 8   m 75 m 
R 
 0.99 
-7
2
A
13 10 m
3.
What is the resistance of a 2 m long copper wire
whose cross-sectional area of 0.2 mm2?
4.
An aluminum wire with a length of 900 m and cross sectional
area of 10 mm2 has a resistance of 2.5 Ω.
What is the resistivity of the wire?
6.
What is the cross-sectional area of a 10Ω copper wire
of length is 10000 meters ?
7.
What is the length of a 10 Ω copper wire whose
diameter is 3.2 mm?
20.3 Resistance and Resistivity
Impedance Plethysmography.
L
L
L2
R 

A
Vcalf L
Vcalf
6. Electric Power
ELECTRIC POWER
When there is current in a circuit as a result of a voltage, the electric
power delivered to the circuit is:
P  IV
SI Unit of Power: watt (W)
Many electrical devices are essentially resistors:
P  I IR   I 2 R
V2
V 
P   V 
R
R
Electrical Power
Let's think about this
another
way...
The water at the top has
GPE & KE.
As the water falls, it loses
GPE and the wheel gets
turned, doing work. When
the water falls to the
bottom it is now slower,
having done work.
Electric circuits are similar.
A charge falls from high voltage to low voltage.
In the process of falling energy may be used (light bulb,
run a motor, etc).
Electric Power
Example 5 The Power and Energy Used in a
Flashlight
In the flashlight, the current is 0.40A and the voltage
is 3.0 V. Find (a) the power delivered to the bulb and
(b) the energy dissipated in the bulb in 5.5 minutes
of operation.
20.4 Electric Power
(a)
P  IV  0.40 A3.0 V  1.2 W
(b)
E  Pt  1.2 W 330 s   4.0 102 J
2.
A toy car's electric motor has a resistance of 17 Ω; find
the power delivered to it by a 6-V battery.
3.
A toy car's electric motor has a resistance of 6 Ω; find
the power delivered to it by a 7-V battery.
4.
What is the power consumption of a flash light bulb
that draws a current of 0.28 A when connected to a 6
V battery?
5.
What is the power consumption of a flash light bulb
that draws a current of 0.33 A when connected to a
100 V battery?
6.
A 30Ω toaster consumes 560 W of power: how
much current is flowing through the toaster?
7.
A 50Ω toaster consumes 200 W of power: how
much current is flowing through the toaster?
8.
When 30 V is applied across a resistor it generates 600
W of heat: what is the magnitude of its resistance?
9.
When 100 V is applied across a resistor it generates
200 W of heat: what is the magnitude of its resistance?
Circuit Diagrams
*Note: Circuit diagrams do not show where each
part is physically located.
7. Series Wiring
There are many circuits in which more than one device is connected to
a voltage source.
Series wiring means that the devices are connected in such a way
that there is the same electric current through each device.
Series Wiring
V  V1  V2  IR1  IR2  I R1  R2   IRS
Series resistors
RS  R1  R2  R3  
Series Wiring
Example 8 Resistors in a Series Circuit
A 6.00 Ω resistor and a 3.00 Ω resistor are connected in series with
a 12.0 V battery. Assuming the battery contributes no resistance to
the circuit, find (a) the current, (b) the power dissipated in each resistor,
and (c) the total power delivered to the resistors by the battery.
Series Wiring
(a)
(b)
RS  6.00   3.00   9.00 
V 12.0 V
I

 1.33 A
RS 9.00 
P  I 2 R  1.33 A  6.00    10.6 W
2
P  I 2 R  1.33 A  3.00    5.31 W
2
(c)
P  10.6 W  5.31 W  15.9 W
Series Wiring
Personal electronic assistants.
8. Parallel Wiring
Parallel wiring means that the devices are
connected in such a way that the same
voltage is applied across each device.
When two resistors are connected in
parallel, each receives current from the
battery as if the other was not present.
Therefore the two resistors connected in
parallel draw more current than does either
resistor alone.
Parallel Wiring
Parallel Wiring
The two parallel pipe sections are equivalent to a single pipe of the
same length and same total cross sectional area.
Parallel Wiring
1
 1 
V V
1 


I  I1  I 2  
 V     V  
R1 R2
 R1 R2 
 RP 
parallel resistors
1
1
1
1
 


RP R1 R2 R3
Parallel Wiring
Example 10 Main and Remote Stereo Speakers
Most receivers allow the user to connect to “remote” speakers in addition
to the main speakers. At the instant represented in the picture, the voltage
across the speakers is 6.00 V. Determine (a) the equivalent resistance
of the two speakers, (b) the total current supplied by the receiver, (c) the
current in each speaker, and (d) the power dissipated in each speaker.
Parallel Wiring
(a)
(b)
1
1
1
3



RP 8.00  4.00  8.00 
I rms
Vrms 6.00 V


 2.25 A
RP 2.67 
RP  2.67 
Parallel Wiring
(c)
(d)
I rms 
Vrms 6.00 V

 0.750 A
R
8.00 
I rms 
P  I rms Vrms  0.750 A 6.00 V   4.50 W
P  I rms Vrms  1.50 A 6.00 V   9.00 W
Vrms 6.00 V

 1.50 A
R
4.00 
Parallel Wiring
Conceptual Example 11 A Three-Way Light Bulb
and Parallel Wiring
Within the bulb there are two separate filaments.
When one burns out, the bulb can produce only
one level of illumination, but not the highest.
Are the filaments connected in series or
parallel?
How can two filaments be used to produce three
different illumination levels?
9. Circuits Wired Partially in Series and Partially in Parallel
20.9 Internal Resistance
Batteries and generators add some resistance to a circuit. This resistance
is called internal resistance.
The actual voltage between the terminals of a batter is known as the
terminal voltage.
20.9 Internal Resistance
Example 12 The Terminal Voltage of a Battery
The car battery has an emf of 12.0 V and an internal
resistance of 0.0100 Ω. What is the terminal voltage
when the current drawn from the battery is (a) 10.0 A
and (b) 100.0 A?
(a)
V  Ir  10.0 A0.010   0.10 V
12.0 V  0.10 V  11.9V
(b)
V  Ir  100.0 A0.010   1.0 V
12.0 V 1.0 V  11.0V
20.10 Kirchhoff’s Rules
The junction rule states that the total
current directed into a junction must
equal the total current directed out of
the junction.
20.10 Kirchhoff’s Rules
The loop rule expresses conservation of energy in terms of the electric
potential and states that for a closed circuit loop, the total of all potential
rises is the same as the total of all potential drops.
20.10 Kirchhoff’s Rules
KIRCHHOFF’S RULES
Junction rule. The sum of the magnitudes of the currents directed
into a junction equals the sum of the magnitudes of the currents directed
out of a junction.
Loop rule. Around any closed circuit loop, the sum of the potential drops
equals the sum of the potential rises.
20.10 Kirchhoff’s Rules
Example 14 Using Kirchhoff’s Loop Rule
Determine the current in the circuit.
20.10 Kirchhoff’s Rules
I 12    6.0 V  I 8.0    24
V

 potentialrises
potentialdrops
I  0.90 A
20.10 Kirchhoff’s Rules
20.10 Kirchhoff’s Rules
Reasoning Strategy
Applying Kirchhoff’s Rules
1. Draw the current in each branch of the circuit. Choose any direction.
If your choice is incorrect, the value obtained for the current will turn out
to be a negative number.
2. Mark each resistor with a + at one end and a – at the other end in a way
that is consistent with your choice for current direction in step 1. Outside a
battery, conventional current is always directed from a higher potential (the
end marked +) to a lower potential (the end marked -).
3. Apply the junction rule and the loop rule to the circuit, obtaining in the process
as many independent equations as there are unknown variables.
4. Solve these equations simultaneously for the unknown variables.
20.11 The Measurement of Current and Voltage
A dc galvanometer. The coil of
wire and pointer rotate when there
is a current in the wire.
20.11 The Measurement of Current and Voltage
An ammeter must be inserted into
a circuit so that the current passes
directly through it.
20.11 The Measurement of Current and Voltage
If a galvanometer with a full-scale
limit of 0.100 mA is to be used to
measure the current of 60.0 mA, a
shunt resistance must be used so that
the excess current of 59.9 mA can
detour around the galvanometer coil.
20.11 The Measurement of Current and Voltage
To measure the voltage between two points
in a circuit, a voltmeter is connected between
the points.
20.12 Capacitors in Series and Parallel
q  q1  q2  C1V  C2V  C1  C2 V
Parallel capacitors
CP  C1  C2  C3  
20.12 Capacitors in Series and Parallel
1
q
q
1 

V  V1  V2  
 q  
C1 C2
 C1 C2 
Series capacitors
1
1
1
1




CS C1 C2 C3
20.13 RC Circuits
Capacitor charging

q  qo 1  e t RC
time constant
  RC

20.13 RC Circuits
Capacitor discharging
q  qo e t RC
time constant
  RC
20.13 RC Circuits
20.14 Safety and the Physiological Effects of Current
To reduce the danger inherent in using circuits, proper electrical grounding
is necessary.