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Chapter 18
Direct Current Circuits
Chapter 18 Objectives
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Compare emf v potential difference
Construct circuit diagrams
Open v Closed circuits
Potential difference in a circuit
Resistors in series
Resistors in parallel
Equivalent resistance
Current across a resistor
Voltage across a resistor
Sources of emf
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Any source that maintains a constant current in a closed circuit is
called an emf source.
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The letters emf used to stand for electromotive force.
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The difference between potential difference and emf is that the
potential difference is the pure movement of charges in space without
any ability to move back on their own.
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Thus, emf is the constant resupplying of charges to create a potential
difference.
The symbol for emf is
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
The SI units for emf is
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V
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But the source does not provide the force, the difference in charge position does.
So we no longer use the long version of the name.
volts
Examples of emf sources are
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batteries
generators
Internal Resistance and emf
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Even though a battery is rated at say 12 V, not all 12 V gets into the circuit.
This is due to the internal resistance of the battery.
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Every emf source has an internal resistance based on the materials that make up the
source and its internal charge path.
Thus the terminal voltage, V, is always less than the advertised emf of a
source.
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V
=
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That would mean there is no load on the source.
Once an external resistance is placed on the source, the circuit is complete
and will allow current to flow both through the internal resistance and the
external resistance.
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r is the internal resistance of the emf source
From the expression, the terminal voltage will be equal to  when the current is
zero.
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 - Ir
So
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The external resistance is also referred to as the load resistance, R.
 = IR + Ir
And  is what we will use to calculate or voltage in a circuit.
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Note: If r << R, then we will disregard r in all calculations!
Schematic Diagrams
• A schematic diagram depicts the construction
of an electrical circuit.
• There is a standard set of symbols used to
eliminate any confusion.
• Each symbol represents a component of an
electrical circuit such as a resistor, a light bulb,
a battery, a switch, etc.
Symbols for Schematic
Diagrams
Component
Wire
Symbol
Explanation
or
The wire connects
the components of
the circuit.
Resistor or Load
A resistor is any
load that disrupts
the flow of
electricity.
Battery
The larger line
represents + charge
and the smaller is .
Derived Symbols
Component
Symbol
Explanation
Switch
The circles represent two
connection points to the
circuit.
Light
A light is treated like a
resistor.
Plug
Looks like the end of a
plug, and like a battery.
Capacitor
Two parallel lines show the
capacitor plates.
Semiconductor
Can control the flow of
electricity
Electrical Circuits
• An electrical circuit is a set of
electrical components connected so
that they provide one or more complete
paths for the movement of charges.
• A closed circuit is one with at least
one continuous loop from one terminal
of the power source to the other.
• An open circuit is one that does not
contain a continuous loop.
Short Circuit
• A short circuit is when there is a direct
path from one terminal to the other
terminal of the power source.
• That direct path contains no resistors,
and therefore provides the least
resistance of flow for the charge
carriers.
• A short circuit increases the current
flow, which can cause damage to the
power source as well as create a great
deal of heat in the wiring.
Schematic Examples
Closed Circuit
Open Circuit
Short Circuit
Resistors in Series
• A series of resistors describes a circuit or
portion of a circuit that provides a single
conducting path of all resistors being in line
with each other.
• When resistors are in series, the amount of
charge over a certain time period entering and
exiting the first resistor is equal to the amount
of charge entering and exiting the second
resistor and so on.
• Thus the total current remains constant
when resistors are in series.
• Series circuits require all elements to conduct.
As soon as there is a gap, the entire circuit
goes out.
Equivalent Resistance
of Resistors in Series
• Since resistors in series line up one after another, the
equivalent resistance of resistors in series is the sum of
the individual resistances.
– The potential drop over the entire circuit must be equal to
the potential difference of the voltage source
• Therefore each resistor will use up as many volts as its
resistance requires to abide by Ohm’s Law.
– Also, since charge must be conserved and it only has one
path to follow, the charge remains constant.
• And if charge is constant, then current is constant!
• The equivalent resistance for series circuit will always
be greater than any individual resistance.
Req = R1 + R2 + R3 + …
Total Current in a
Series Circuit
• To find the total current in a series
circuit, simplify the circuit to a
single equivalent resistance.
• Then use ΔV = IR to calculate the
current.
ΔV
I=
Req
Potential Difference
Across Each Resistor
• Because the current in each
resistor is equal to the total current
in the circuit, you can use ΔV = IR to
calculate the potential difference across
each resistor.
ΔV1 = IR1
ΔV2 = IR2
Resistors in Parallel
• A parallel circuit describes two or more components in a circuit
that connected across common points providing separate
conducting paths for the charges.
– The parallel nature comes from looking at schematic diagrams
and showing the alternate paths for charges to flow as being
parallel to each other, whether they physically are or not.
• Due to the differing paths, the charge through each path will
sum to the total charge of the circuit.
– Therefore, the current in each path will sum to the total current of
the entire circuit.
• The potential difference across the resistors in parallel will
remain constant.
• If there is a gap in a parallel circuit, the rest of the circuit will
still conduct.
Equivalent Resistance
of Resistors in Parallel
• Observe what happens to ΔV = IR when
we solve for the current.
– We solve for current because the sum of
each branch of current gives the total.
Itotal = ΔV1 + ΔV2
R2
R1
• Notice how the inverses of the resistances are added together.
•The equivalent resistance of a parallel circuit is always less
than the smallest resistance of the group.
1
1
1
1
=
+
+
+…
Req
R2
R1
R3
Current in Individual
Resistors of a Parallel Circuit
• The current in each resistor is
found by
I=
ΔV
Rn
• The potential difference remains constant.
Series and Parallel
Schematics
Series
Parallel
Assembly of Circuits
• A series circuit connects
the resistors one after
another.
• So the positive lead
should connect to one
side of the resistor.
• The negative lead goes
from the other side of the
resistor to one side of
the next resistor.
• The circuit should look
like one continuous loop
of alternating positive
and negative leads.
• A parallel circuit
connects the resistors as
parts of separate
branches of the circuit.
• All the positive leads
branch off from the same
junction point.
• The negatives then join
at the same junction
point of their own.
• Simply put, positive
connects to positive for
each resistor.
Kirchhoff’s Rules
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Gustav Kirchhoff (1824-1887) came up with an order
of operations for electrical circuits
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The sum of the currents entering any junction must
equal the sum of the currents leaving that junction.
1.
2.
Called the junction rule.
The sum of the potential differences across all the
elements around any closed-circuit loop must be zero.
2.
Called the loop rule.
Applying Kirchhoff’s Rules
1.
Draw the circuit diagram in a way that is simple to
understand.
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Try to draw each resistor sequence so it is either vertical
or horizontal.
You must designate a current flow for each loop.
1.
If you designate it incorrectly, it will show up as a negative
value, but the magnitude will still be correct.
1.
2.
3.
Apply the junction rule for every new junction
individually.
Apply Kirchhoff’s loop rule for each loop necessary in
the circuit.
3.
4.
If this is the case, leave it negative for all calculations
later on.
Be sure to identify whether it is a voltage drop of voltage
gain as you pass through a voltage source.
Solve the equations simultaneously for the unknown
quantities.
RC Circuits
• Once a capacitor is inserted into the circuit,
the current is no longer constant.
• The current will gradually decrease as the
capacitor charges.
– Once the capacitor is fully charged, the current will
be zero.
• q = Q(1 - e(-t / RC))
• But this takes time to charge the capacitor
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 = RC
• Where  is the time constant for a capacitor to
charge to 63.2% of its maximum equilibrium charge.
– Plug t =  = RC and notice what happens!
Circuit Breaker v Fuse
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A circuit breaker is typically
used in large circuit
applications such has a house
or building.
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The typical tripping level for a
circuit breaker is 15 A.
A circuit breaker acts like a
switch to open the circuit when
an overload is sensed.
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The switch consists of a
bimetallic strip that heats up
as current travels through the
circuit.
When the heat is too much,
the strip pushes on the switch
itself to open the circuit.
The circuit cannot be closed
until the strip has cooled
down.
A fuse is typically used in
small circuits that need a
quick break in the current
flow.
– A fuse can be used for a
large range of current
levels.
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A fuse is a small metallic
strip that is part of the
current path.
– When the current level
becomes too high, the
fuse will burn out from the
excess heat.
– The metallic strip will melt
or break away from the
heat, opening the circuit.
– The fuse must be replaced
with a new one if it has
blown.