Download Current Electricity

Current electricity
•
•
•
•
•
Lesson 1: electric current
Lesson 2: Electrical Resistance
Lesson 3: Ohm’s Law
Lesson 4: Electrical Power
Lesson 5: Circuit, Circuit Symbols and Circuit
Connections
• Lesson 6: Series Circuits
• Lesson 7: Parallel Circuits
Lesson 1: Electric Current
1. The Electric Circuit and its
Requirements
2. Electric Current
3. Common Misconceptions Regarding
Electric Circuits
How to light a light bulb
• Objective: light a light bulb
• Material: one battery, one wire, one light bulb.
• What you must do in order for the light bulb to work?
Light Bulb Anatomy
• A light bulb is a device consisting of a
filament attached to two wires. The
wires and the filament are conducting
materials which allow charge to flow
through them. One wire is connected to
the ribbed sides of the light bulbs. The
other wire is connected to the bottom
base of the light bulb. The ribbed edge
and the bottom base are separated by an
insulating material which prevents the
direct flow of charge between the
bottom base and the ribbed edge. The
only pathway by which charge can make
it from the ribbed edge to the bottom
base or vice versa is the pathway which
includes the wires and the filament.
+
What is an Electric Circuit?
A circuit is simply a closed loop through which charges can
continuously move.
The Requirement of a circuit
1. There must be a closed
conducting loop in the external
circuit which stretches from the
high potential, positive terminal
to the low potential, negative
terminal.
2. 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.
Electric Current
• If the two requirements of an electric circuit are met,
then charge will flow through the external circuit.
This flow of charge or current, is the rate at which
charge flows past a point on a circuit.
Current is a rate quantity. Like velocity - the rate
at which an object changes its position.
Acceleration - the rate at which an object
changes its velocity. And power - the rate at
which work is done on an object. In every case of
a rate quantity, the mathematical equation
involves some quantity over time.
Definitions
• current: RATE OF CHARGE FLOW
• unit: C/s or AMPERE
• requires:
• POTENTIAL DIFFERENCE
• PATH FOR FLOW
q
I
t
Example #1
• 100 coulombs of charge pass through point A in 4.0
seconds.
– What is the rate of current flow through point A?
I = Δq / t
I = 100 C / (4.00 s)
I = 25 A
A
Example #2
• During a thunderstorm a lightning strike transfers
15.0 coulombs of charge in 10.0 milliseconds.
– What was the electrical current produced in the strike?
I = Δq / t
I = 15.0 C / (10 x 10-3 s)
I = 1.5 x 105 A
Example #3
• A wire carries a current of 50 amperes.
– How much charge flows through the wire in 10 seconds?
– How many electrons pass through the wire in 10 seconds?
I = Δq / t
50 A = q / (10 s)
q = 500 C
3.125 x 1021 e
example
• If charge flowing at the rate of 2.50 × 1016 elementary charges
per second. What is the electric current?
q
I
t
Conventional Current Direction
The direction of an
electric current is by
convention the
direction in which a
positive charge would
move.
Current versus Drift Speed
Q
I
t
Current has to do with the number of coulombs of
charge that pass a point in the circuit per unit of
time.
• Drift speed refers to the average
distance traveled by a charge carrier per
unit of time.
Even though the drift speed is extremely
slow, the current could be big. This is
because there are many, many charge
carriers moving at once throughout the
whole length of the circuit.
The Nature of Charge Flow
• We know that the average drift speed of an electron is very,
very slow, why does the light in a room or in a flashlight light
immediately after the switched is turned on?
• Charge carriers in the wires of electric circuits are electrons.
They are already there supplied by the atoms of the wire. Once
the switch is turned to on, there is an electric potential
difference established across the two ends of the external
circuit. The electrons begin moving along a zigzag path in their
usual direction. Thus, the flipping of the switch causes an
immediate response throughout every part of the circuit,
setting charge carriers everywhere in motion in the same net
direction.
• While the actual motion of charge carriers occurs with a slow
speed, the signal that informs them to start moving travels at a
fraction of the speed of light.
Only energy can be used up, charge
can never be used up
• The charge carriers never become consumed
or used up. While the energy possessed by
the charge may be used up, the charge
carriers themselves do not disintegrate,
disappear or otherwise become removed from
the circuit. And there is no place in the circuit
where charge carriers begin to pile up or
accumulate. The rate at which charge enters
the external circuit on one end is the same as
the rate at which charge exits the external
circuit on the other end.
Lesson 2 - Electrical Resistance
1. Resistance
2. Ohm's Law
3. Power Revisited
Definitions
• resistance: OPPOSITION TO CURRENT
• unit: Ω
• factors that change resistance:
• resistivity: MATERIAL
• length
• cross-sectional area
• temperature
R
L
A
To build
anwire
“ideal”
conductor with
L - the length
of the
(meters),
the smallest
possible
resistance
A - the cross-sectional
area
of the wire
(m2),
ρ - the resistivity
of the material
(in Ω•meter).
you would
select one
that is:
R - the resistance of the wire (in Ω)
LOW RESISTIVITY, SHORT, WIDE,
COLD
Resistance Factors
R
R
R
L
A
ρ
A
R
R
L
Temp.
Example #1
• Determine the resistance of a 1.0 meter long copper
wire with a cross-sectional area of 0.01 meter2.
R = ρL / A
R = (1.72 x 10-8 Ω·m)(1.0 m) / (0.01 m2)
R = 1.72 x 10-6 Ω
Example #2
• A piece of wire that has a length of 5.0 x 107 meters
and a cross-sectional area of 0.025 meter2 has a
resistance of 31.8 ohms.
– What is the composition of this wire?
R = ρL / A
ρ = RA / L
ρ = (31.8 Ω)(0.025 m2) / (5.0 x 107 m)
ρ = 1.59 x 10-8 Ω·m
example
•
An incandescent light bulb is supplied with a
constant potential difference of 120 volts. As the
filament of the bulb heats up,
1. What happens to the resistance?
2. What happens to the current?
example
•
1.
2.
3.
4.
If the cross-sectional area of a metallic
conductor is halved and the length of the
conductor is doubled, the resistance of the
conductor will be ______________.
halved
doubled
unchanged
quadrupled
example
•
A 12.0-meter length of copper wire has a resistance
of 1.50 ohms. How long must an aluminum wire
with the same cross-sectional area be to have the
same resistance?
example
• Pieces of aluminum, copper, gold, and silver
wire each have the same length and the same
cross-sectional area. Which wire has the
lowest resistance at 20°C?
Lesson 3 – Ohm’s Law
Know:
– Equation for Ohm’s Law.
Understand
– Current is directly proportional to voltage and inversely
proportional to electrical resistance.
Be able to
– Determine current; voltage; resistance; and/or power in a
system with a single resistor.
- Sketch/interpret graphs of relating voltage; current;
resistance;
- Determine whether or not a particular object obeys Ohm’s
Law.
Ohm’s Law
• Voltage results in current flow
• More voltage = more current
• Resistance opposes current flow
• More resistance = less current
V
I
R
Resistance: R = V / I
• R is the slope of a potential difference vs. current
graph. The resistance is a constant for a metallic
conductor at constant temperature.
V
V
Slope is resistance
I
Ohmic material
I
Non-Ohmic material
Graphs: I vs. V and I vs. R
V
I
R
I vs. V
1
slope 
R
I
V
Current and potential
difference have a direct
relationship. The slope is
equivalent to the reciprocal of
the resistance of the resistor.
I vs. R
I
R
Current and
resistance have an
inverse relationship
Ohm's Law as a Predictor of Current
V
I
R
• The current in a circuit is directly proportional to the
electric potential difference impressed across its ends
and inversely proportional to the total resistance offered
by the external circuit.
• The greater the battery voltage (i.e., electric potential
difference), the greater the current. a twofold increase in
the battery voltage would lead to a twofold increase in
the current (if all other factors are kept equal).
• The greater the resistance, the less the current. An
increase in the resistance of the load by a factor of two
would cause the current to decrease by a factor of two to
one-half its original value.
Check Your Understanding
1. Which of the following will cause the current
through an electrical circuit to decrease?
Choose all that apply.
a. decrease the voltage
b. decrease the resistance
c. increase the voltage
d. increase the resistance
Check Your Understanding
2. A copper wire is connected across a constant
voltage source. The current flowing in the
wire can be increased by increasing the
wire's
a. cross-sectional area
b. length
c. resistance
d. temperature
Check Your Understanding
3. A series circuit has a total resistance of 1.00 × 102
ohms and an applied potential difference of 2.00 ×
102 volts. What is the amount of charge passing any
point in the circuit in 2.00 seconds?
Check Your Understanding
4. A long copper wire was connected to a voltage
source. The voltage was varied and the current
through the wire measured, while temperature was
held constant. Using the graph to find the resistance
of the copper wire.
Check Your Understanding
• A student conducted an experiment to determine the resistance
of a light bulb. As she applied various potential differences to the
bulb, she recorded the voltages and corresponding currents and
constructed the graph below. The student concluded that the
resistance of the light bulb was not constant.
5.
What evidence from the graph supports the student’s
conclusion?
6.
According to the graph, as the
potential difference increased,
what happens to the
resistance of the light bulb?
Check Your Understanding
7.
a.
b.
c.
d.
A circuit consists of a resistor and a battery. Increasing the
voltage of the battery while keeping the temperature of the
circuit constant would result in an increase in
current, only
resistance, only
both current and resistance
neither current nor resistance
Check Your Understanding
8. Sketch a graph that best represents the relationship
between the potential difference across a metallic
conductor and the electric current through the
conductor
a. At constant temperature T1
b. At a higher constant temperature T2.
V
I
Check Your Understanding
9. A 1.5-volt, AAA cell supplies 750 milliamperes of
current through a flashlight bulb for 5.0 minutes,
while a 1.5-volt, C cell supplies 750 milliamperes of
current through the same flashlight bulb for 20.
minutes. Compared to the total charge transferred
by the AAA cell through the bulb, the total charge
transferred by the C cell through the bulb is
a. half as great
b. twice as great
c. the same
d. four times as great
Example #1
• A potential difference of 25.0 volts is supplied to a
circuit with 100 ohms of resistance.
– How much current flows through this circuit?
I=V/R
I = 25.0 V / 100 Ω
I = 0.25 A
Example #2
• A current of 2.0 amperes flows through a 10 ohm
resistance.
– What voltage must be applied to this resistance?
I=V/R
V = IR
V = (2.0 A)(10 Ω)
V = 20 V
Example #3
• A 10 volt battery establishes a current of 5.0 amperes
in a circuit.
– What is the resistance of this circuit?
I=V/R
R=V/I
R = (10 A) / (5.0 A)
R = 2.0 Ω
Lesson 4: Electrical Power
Know:
• Definition and equation for electrical power.
Understand
• Power is directly proportional to both voltage and current.
Be able to
• Determine power in a system with a single resistor.
• Sketch/interpret graphs of relating voltage; current;
resistance and power with each other (assuming that all
other variables are fixed.)
Power: Putting Charges to Work
Electrical devices, generally referred to as loads, have power ratings.
A 1200 W hair dryer indicates it
transfers 1200 Joules of electrical
energy to heat, wind, sound energy
in 1 second.
Energy
Power 
time
The unit of power is watt.
1 watt = 1 joule / second
• A circuit with a battery and a wire leading from positive to negative
terminal without a load would lead to a high rate of charge flow.
Such a circuit is referred to as a short circuit. It would heat the wires
to a high temperature and drain the battery of its energy rather
quickly.
Power Law
• Moving electrons (current) requires ENERGY
• How much energy gets used depends on:
• Strength of push – VOLTAGE
• Rate of flow – CURRENT
V
I
R
P  IV
2
V
2
P  IV 
I R
R
Example #1
• A 12 volt battery is connected to a circuit which
allows 10 amperes of current to flow.
– What is the power output of this circuit?
P = IV
P = (12 V)(10 A)
P = 120 W
Example #2
• A 100 watt light bulb is connected to a 120 volt power
supply.
– What amount of current must pass through the light bulb?
P = IV
100 W = (120 V) I
I = 0.833 A
Example #3
• A 2.0 ampere current passes through a circuit with a
300 ohm resistance.
– What is the power generated in this circuit?
P = I2 R
P = (2.0 A)2 (300 Ω)
P = 1200 W or 1.2 kW
Different units for power
P = I2•R
P = V2/R
P = V·I
relate current and resistance to power, notice double
importance of current. Unit: A2∙Ω
relate potential difference and resistance to power,
notice double importance of potential difference.
Unit: V2/Ω
relate potential difference and current to power.
Notice that both have equal importance. Unit: V∙A
Warning:
While these three equations provide one with
convenient formulas for calculating unknown
quantities in physics problems, one must be careful
to not misuse them by ignoring conceptual
principles regarding circuits.
Check your understanding
1. If a 60-watt bulb in a household lamp was replaced
with a 120-watt bulb, then how many times greater
would the current be in that lamp circuit?
Check your understanding
2.
a.
b.
c.
d.
Which is a unit of electrical power?
volt/ampere
ampere/ohm
ampere2/ohm
volt2/ohm
Graphs of power vs. R, I, V
• P = VI = I2R = V2/R
• When V is constant: P = VI; P = V2/R – common house hold
appliances
P
P
Inverse, high R, low P
V is slope
R
I
• When R is constant: P = I2R; P = V2/R – same appliances
P
P
Direct squared
I
Direct squared
V
Check your understanding
3. As the resistance of a constant-voltage circuit
is increased, the power developed in the
circuit
a. decreases
b. increases
c. remains the same
Check your understanding
4. The potential difference applied to a circuit element remains
constant as the resistance of the element is varied. Graph power
(P) vs. resistance (R) for this circuit.
P
R
Check your understanding
5. Graph the relationship between the electrical
power and the current in a resistor that
obeys Ohm’s Law.
P
I
Check your understanding
6. An electric motor uses 15 amperes of current
in a 440-volt circuit to raise an elevator
weighing 11,000 Newtons. What is the
average speed attained by the elevator?
example
7. To increase the brightness of a desk lamp, a
student replaces a 60-watt light bulb with a
100-watt bulb. Compared to the 60-watt
bulb, the 100-watt bulb has
a. less resistance and draws more current
b. less resistance and draws less current
c. more resistance and draws more current
d. more resistance and draws less current
Check Your Understanding
8. Which would be thicker (wider) - the filament of a 60-Watt
light bulb or the filament of a 100-W light bulb? Explain.
9. Calculate the resistance and the current of a 7.5-Watt night
light bulb plugged into a US household outlet (120 V).
Electrical energy
• E = P∙t = V∙I∙t = I2∙R∙t = (V2/R)∙t
• The SI unit for energy is Joule.
• 1 joule = (1 Newton)(1 meter)
= (1 kg∙m/s2)(1 meter)
= 1 kg∙m2/s2
The kilowatt-hour
• Electrical utility companies provide energy for homes
charge those homes for the electrical energy they
used. A typical bill will contain a charge for the
number of kilowatt-hours of electricity which were
consumed.
• How many Joules is in one kWh?
Check your understanding
1. Your 60-watt light bulb is plugged into a 110-volt household
outlet and left on for 10 hours. The utility company charges
you $0.20 per kWh. What is the cost?
2. A current of 0.40 ampere is measured in a 150 ohm resistor,
how much energy is expended by the resistor in 20. seconds?
3. An electric dryer consumes 6.0 × 106 joules of energy when
operating at 220 volts for 30. minutes. During operation, how
much current does the dryer draws approximately?
Energy can be transformed, but is conserved
• The purpose of every circuit is to supply the energy
to operate various electrical devices. These devices
are constructed to convert the energy of flowing
charge into other forms of energy (e.g., light,
thermal, sound, mechanical, etc.). Use complete
sentences to describe the energy conversions that
occur in the following devices.
1. Windshield wipers on a car
2. Defrosting circuit on a car
3. Hair dryer
Rechargeable Batteries
• Rechargeable batteries has nothing to do with charges.
• Rechargeable batteries rely upon a reversible reaction, turning the
chemical products back into chemical reactants within the cell.
Alert: Statement True or False?
1. When an electrochemical cell no longer works, it is out of charge
and must be recharged before it can be used again.
2. An electrochemical cell can be a source of charge in a circuit. The
charge which flows through the circuit originates in the cell.
3. Charge becomes used up as it flows through a circuit. The
amount of charge which exits a light bulb is less than the amount
which enters the light bulb.
4. Charge flows through circuits at very high speeds. This explains
why the light bulb turns on immediately after the wall switch is
flipped.
5. The local electrical utility company supplies millions and millions
of electrons to our homes everyday.
Example
• A 12.0-meter length of copper wire has a
resistance of 1.50 ohms. How long must an
aluminum wire with the same cross-sectional
area be to have the same resistance?
Example
• Calculate the resistance of a 1.00-kilometer
length of nichrome wire with a cross-sectional
area of 3.50 × 10-6 meter2 at 20°C.
• The tendency to give attention to units is an
essential trait of any good physics student.
• Many of the difficulties associated with
solving problems may be traced back to the
failure to give attention to units. As more and
more electrical quantities and their respective
metric units are introduced, it will become
increasingly important to organize the
information in your head.
Quantities, Symbols, Equations and Units!
Quantity
Symbol
Equations
Standard
Metric
Unit
Potential Difference
(a.k.a. voltage)
V
V= W / Q
V=I•R
Volt (V)
J/C
Current
I
I=Q/t
I=V/R
Amperes (A)
C/s
V/Ω
Power
P
P=W/t
P = V∙I
P = V2/R
P = I2 R
Watt (W)
J/s
V∙A
V/ Ω2
A2∙Ω
Resistance
R
R = ρ•L / A
R=V/I
Ohm (Ω )
V/A
Energy
W
W=V•Q
W=P•t
Joule (J)
V•C
W•s
Other
Units
Lesson 5: Circuit, Circuit Symbols and
Circuit Connections
1. What is a circuit?
2. Circuit Symbols and Circuit Diagrams
3. Two Types of Connections
What is a circuit?
• A continuous loop through which current flows
from an area of high voltage to a an area of low
voltage.
Circuit Symbols
Voltage sources
Resistances
Other Elements
Measurement
Devices
Circuit Elements – Measuring Devices
voltmeter
ammeter
Measures: VOLTAGE
Resistance: HIGH
Connect to circuit: OUTSIDE
Measures CURRENT
Resistance: LOW
Connect to circuit: INSIDE
Meters in a Circuit
V
5V
R = 2.5Ω
V
2A
0V
Voltmeter
measures
RELATIVE
Potential
differences
from OUTSIDE
the circuit
2A
A
A
V = 5V
V
5V
0V
V
Ammeter
measures
Current flow
INSIDE
the circuit
Meters in a circuit
V
A
V
A
Two types of connections
• Three D-cells are placed in a battery pack to power a
circuit containing three light bulbs
Schematic Diagram of Circuit
Only use circuit
symbols in your
reference table to draw
the circuits
Schematic Diagram of Circuit
Series and Parallel connections
• These two examples illustrate the two common types of
connections made in electric circuits. When two or more
resistors are present in a circuit, they can be connected in
series or in parallel.
For series circuits
• http://phet.colorado.edu/en/simulation/circuitconstruction-kit-dc
1. As more resistors are added the overall
current within the circuit decreases.
2. This decrease in current is consistent with the
conclusion that the overall resistance
increases.
3. If one of three bulbs in a series circuit is
unscrewed from its socket, then the other
bulbs immediately go out.
For parallel circuits
• http://phet.colorado.edu/en/simulation/circuitconstruction-kit-dc
1. As the number of resistors increases, the overall
current also increases.
2. This increase in current is consistent with a
decrease in overall resistance. Adding more
resistors in a separate branch has the unexpected
result of decreasing the overall resistance!
3. If an individual bulb in a parallel branch is
unscrewed from its socket, other bulbs are not
effected.
Check Your Understanding
1. Observe the electrical wiring below. Indicate whether
the connections are series or parallel connections.
Explain each choice.
2. Two electric circuits are diagrammed below. For
each circuit, indicate which two devices are
connected in series and which two devices are
connected in parallel.
In series? ______________
In parallel? ______________
In series ________________
In parallel? ______________
Lesson 6 Series Circuits
Be able to
1. Sketch diagrams of series circuits including proper placement
of meters.
2. VIR charts and Ohm’s Law to solve series circuits problems.
3. Determine the power or electrical energy used by a circuit
component or an entire circuit.
4. Determine the effect of adding or removing resistors to the
rest of a circuit.
Definitions
• series circuit – a circuit in which two or more elements
are connected end-to-end so that a single loop of current
is formed.
1. Same current flows through the
all resistor.
2. The potential difference of
across the bigger resistor is
higher than the potential
difference across the smaller
resistor.
3. By the time each charge makes
it back to the battery, it has lost
all the electrical energy given to
it by the battery.
Series Circuit Rules
• equivalent Resistance – more resistors = more resistance
• RT = R1 + R2 + …
• current – same throughout circuit
• IT = I 1 = I 2 = …
Req is same as RT
• voltage – voltages add up
• VT = V1 + V2 + …
Veq is same as VT
Ieq is same as IT
• All circuit components and the circuit as a whole must
obey Ohm’s Law
5.0 Ω
8.0 Ω
2.0 Ω
R1
R2
R3
7.5 V
V (V)
R1
R2
R3
Req
I (A)
R (Ω)
2.5
0.5
5.0
4.0
0.5
8.0
1.0
0.5
2.0
7.5
0.5
15
50 Ω
120 Ω
150 Ω
R1
R2
R3
1.5A
V (V)
R1
R2
R3
Req
I (A)
R (Ω)
75
1.5
50
180
1.5
120
225
1.5
150
480
1.5
320
Example
• A series circuit has a total resistance of 1.00 x
102 ohms and an applied potential difference
of 2.00 x 102 volts. What is the amount of
charge passing any point in the circuit in 2.00
seconds?
I = V / R = 2.00 x 102 V / 1.00 x 102 Ω
I = 2.00 A
I=Q/t
2.00 A = Q / 2.00 s
Q = 4.00 C
Lesson 7 Parallel Circuits
Be able to
1. Sketch diagrams of parallel circuits including proper placement
of meters.
2. VIR charts and Ohm’s Law to solve parallel circuits problems.
3. Determine the power or electrical energy used by a circuit
component or an entire circuit.
4. Determine the effect of adding or removing resistors to the
rest of a circuit.
Definitions
• parallel circuit – a circuit in which two or more
elements are connected so that each has its own
current loop.
1. More current flows through
the smaller resistor. (More
charges take the easiest path.)
2. The potential difference of
different resistors are the
same, they all have the same
drop.
3. By the time each charge makes
it back to the battery, it has
lost all the electrical energy
given to it by the battery.
Parallel Circuit Rules
• equivalent Resistance – more resistors = less resistance
• 1/Req = 1/R1 + 1/R2 + …
• current – currents add up
• I = I1 + I2 + …
• voltage – voltages same for each resistor
• V = V1 = V2 = …
• All circuit components and the circuit as a whole must
obey Ohm’s Law
Current
• In a parallel circuit, charge divides up into separate branches
such that there can be more current in one branch than there is
in another. Nonetheless, when taken as a whole, the total
amount of current in all the branches when added together is
the same as the amount of current at locations outside the
branches.
Itotal = I1 + I2 + I3 + ...
Junction Rule
• The total current flowing into and out of a junction must
be the same
6.0? A
10 A
4.0 A
Junction Rule
6.0 A
6.0? A
4.0? A
2.0 A
10 A
Example
•
1.
2.
3.
4.
The diagram shows the current in three of the branches
of a direct current electric circuit. The current in the
fourth branch, between junction P and point W, must be
1 A toward point W
1 A toward point P
7 A toward point W
7 A toward point P
Example
•
The diagram shows a current in a segment of
a direct current circuit. What is the reading
of ammeter A?
Equivalent Resistance
• The equivalent resistance (total resistance) of a circuit
is the amount of resistance which a single resistor
would need in order to equal the overall effect of the
collection of resistors which are present in the circuit.
For parallel circuits, the mathematical formula for
computing the equivalent resistance (Req) is
1
1
1
1
 

Req R1 R2 R3
where R1, R2, and R3 are the resistance values of the
individual resistors which are connected in parallel.
• For parallel circuit, adding more resistors you add the
less resistance you have.
Example – determine equivalent R
1
1
1
1



Req 5 7 12
Req  2.3
Note: the equivalent resistance is less than any single resistance in the
circuit.
Example
•
1.
2.
3.
4.
Resistors R1 and R2 have an equivalent
resistance of 6 ohms when connected as
shown. What is the resistance of R1?
3 ohms
4 ohms
5 ohms
8 ohms
Since the equivalent resistance is smaller
than any single resistance in the parallel
circuit, the answer is 8 ohms
Example
• Resistors R1 and R2 have the same resistance. When
they are connected together as shown, they have an
equivalent resistance of 4 ohms. What is the
resistance of R1?
Since R1 = R2
1/4 Ω = 1/R1 + 1/R1 = 2/R1
R1 = 8 Ω
Note: the individual resistance is bigger than
the total resistance in the parallel circuit.
Voltage Drops for Parallel Branches
• The total voltage drop in the external circuit is equal to the
gain in voltage as a charge passes through the internal circuit.
In a parallel circuit, a charge does not pass through every
resistor; rather, it passes through a single resistor. Thus, the
entire voltage drop across that resistor must match the
battery voltage. It matters not whether the charge passes
through resistor 1, resistor 2, or resistor 3, the voltage drop
across the resistor which it chooses to pass through must
equal the voltage of the battery. Put in equation form, this
principle would be expressed as
Vbattery = V1 = V2 = V3 = ..
All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law
I1 = V / R1
I2 = V / R2
I3 = V / R3
V
I eq 
Req
V (V)
R1
R2
R3
Req
I (A)
R (Ω)
60
2.0
30
60
2.0
30
60
2.0
30
60
6.0
10
R3 = 30 Ω
R2 = 30 Ω
R1 = 30 Ω
60 V
0.5 A
V (V)
R1
R2
R3
Req
I (A)
R (Ω)
5.0
0.25
20
5.0
0.1
50
5.0
0.5
10
5.0
0.85
5.9
R3 = 10 Ω
R2 = 50 Ω
R1 = 20 Ω
Example
• In the diagram, what is the potential
difference across the 3.0-ohm resistor?
Example
•
Circuit A and circuit B are shown in the diagram.
Compared to the total resistance of circuit A, the
total resistance of circuit B is
1. less
2. greater
3. the same
Example
• In the diagram of a parallel circuit, ammeter A
measures the current supplied by the 110-volt
source. What is the current measured by
ammeter A?
11 A
Example
• Two resistors are connected to a source of voltage as
shown in the diagram. At which position should an
ammeter be placed to measure the current passing
only through resistor R1?
1. position 1
2. position 2
3. position 3
4. position 4
Example
• Three ammeters are placed in a circuit as
shown in the diagram. If A1 reads 5.0 amperes
and A2 reads 2.0 amperes, what does A3 read?
3A
Example
• In the circuit shown in the diagram, which is
the correct reading for meter V2?
Example
• Which circuit could be used to determine the total
current and potential difference of a parallel circuit?
A
C
B
D
Example
• In the circuit shown in the diagram, what is
the potential difference of the source?
Example
• Which circuit below would have the lowest
voltmeter reading?
A
B
C
D
Example
•
1.
2.
3.
4.
In which pair of circuits shown in the diagram could the
readings of voltmeters V1 and V2 and ammeter A be
correct?
A and B
B and C
C and D
A and D
Example
•
1.
2.
3.
4.
Which statement about ammeters and voltmeters is
correct?
The internal resistance of both meters should be
low.
Both meters should have a negligible effect on the
circuit being measured.
The potential drop across both meters should be
made as large as possible.
The scale range on both meters must be the same.
Example
•
1.
In the diagram below, lamps L1 and L2 are connected to a
constant voltage power supply. If lamp L1 burns out,
What will happen to the equivalent resistance of the circuit?
2.
What will happen to the total current of the circuit?
3.
What will happen to the brightness of L2 ?
Example
• Identical resistors (R) are connected across the same 12-volt
battery. Which circuit uses the greatest power?
A
C
B
D
Lab 15 – Resistance
PURPOSE:
1. Determine the relationship between Resistance and the length of the wire
2. Determine the relationship between Resistance and the area of the wire
3. Determine resistivity of the wire
MATERIAL:
• Nichrome wire boards, multipurpose meter, ruler, graph paper
DATA:
diameter _________ m
Area __________m2
Length (m)
R (Ω)
L (m)
Resistance ∙Area
(Ω∙m2)
Length _________ m
R (Ω)
Area (m2)