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PHY 101 Lecture #9
Electrical circuits
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PHY 101 Lecture #9:
Electrical Circuits
Prof. Peter R. Saulson
saulson@physics.syr.edu
http://physics.syr.edu/courses/PHY101/
Office Hrs: Tues 10 11:30, Physics 263-4, 3-5994 PHY 101 Lecture #9
Electrical circuits
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Outline
1. Intuition about voltage and current
2. A simple circuit
3. Resistors and Ohms Law
4. Series and parallel circuits PHY 101 Lecture #9
Electrical circuits
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Electrical circuits
Magic of conductors: charge can move freely
inside them.
Steady motion of charge requires:
Steady source of electrical potential difference
between two terminals
Complete circuit connecting the terminals.
Circuit can be a simple component connecting
battery terminals, or several components. PHY 101 Lecture #9
Electrical circuits
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Batteries
Electric potential difference (voltage difference)
between two points is easy to set, using a
battery.
Maintains a fixed voltage between its two terminals.
Many kinds of battery available, with voltages
between 1 and 24 volts.
Later, we will study the chemistry that makes
them work. PHY 101 Lecture #9
Electrical circuits
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Simple circuit
battery
component
Here, a single
component
completes the
circuit from one
battery terminal to
the other.
One such
component is a
resistor. A resistor
lets current flow,
but not freely as a
wire would. PHY 101 Lecture #9
Electrical circuits
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Intuition about voltage
Voltage is sometimes called electromotive
force. It makes circuits go.
A ball falls down because of gravitational force
(or equivalently, because it can give up U
grav
.)
Currents flow in a circuit because they are given
a path from high voltage to low voltage. PHY 101 Lecture #9
Electrical circuits
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More intuition about voltage
1. Voltages are always measured with respect to
some reference point in a circuit.
Sometimes we refer to voltage drop or voltage
difference between two points.
Other times, we give the voltage with respect to a
reference point called ground, (usually the
negative terminal of the battery.)
2. Along any wire (or other good conductor),
the voltage is a constant.
Voltage drops occur across components, such as
resistors. PHY 101 Lecture #9
Electrical circuits
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Intuition about current
Electric current is the flow (i.e. motion) of
electric charge through a circuit.
It is the kind of motion associated with
electricity.
A circuit with a current has something
happening, while a circuit with no current is
static, like a ball sitting still. PHY 101 Lecture #9
Electrical circuits
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More intuition about current
Electric current in a circuit is like water moving
through pipes.
When current comes to a point where it can
take two paths, it divides.
Sum of the currents in the two paths equals the
current that arrived at the split.
When two circuit paths combine, the total
current after the join is the sum of the two
currents that arrived. PHY 101 Lecture #9
Electrical circuits
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What happens in this
simple circuit
+
resistor
The battery
determines voltage
across the resistor.
Current can flow
(but not freely)
from plus terminal to
minus terminal of
battery. PHY 101 Lecture #9
Electrical circuits
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Measuring voltage in a circuit
+
V
Voltmeter across
resistor reads voltage
drop between the ends
of the resistor.
(Voltage always
measured from one
point in circuit to
another.) PHY 101 Lecture #9
Electrical circuits
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Measuring current in a circuit
+
A
Ammeter in circuit reads
current flow through
resistor.
Ammeter acts like a
smart wire, conducts
electric current while
telling you how much.
If you want to tell the
current, insert an
ammeter in the middle
of a wire. PHY 101 Lecture #9
Electrical circuits
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Ohms Law
Battery determines voltage V across resistor.
For a given resistor, current I will flow,
according to Ohms Law,
where R is the resistance of that resistor.
In other words, I = V/R is the current in the
circuit.
The SI unit of resistance is the ohm, abbreviated
by the symbol .
,
IR
V
= PHY 101 Lecture #9
Electrical circuits
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Numerical examples of resistance
If batterys voltage is 4.6 V and R = 100 , then
current through the circuit is
I = V/R = 4.6 V / 100 = 0.046 A = 46 mA.
Resistance of a good wire can be much less than
1 .
A resistor of 1 M is still a much better
conductor than the air around the circuit. PHY 101 Lecture #9
Electrical circuits
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Intuition about resistance
Resistance is a measure of how readily current
is allowed to flow.
Voltage drops across a resistor, but doesnt
drop noticeably across a good wire.
When you read a circuit diagram, all spots
connected directly by wires have the same
voltage. PHY 101 Lecture #9
Electrical circuits
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Series connection of two resistors
Two resistors connected
end to end.
The current that flows
through one resistor
must flow through the
other. PHY 101 Lecture #9
Electrical circuits
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Current
in series connection Current has only one
possible path around the
circuit.
Ammeter in each place
reads the same current. PHY 101 Lecture #9
Electrical circuits
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Voltage in series connection
V
V
Voltage drop across one
resistor plus voltage
drop across second
resistor equals voltage
difference between
battery terminals.
I=V/R for first resistor;
must equal I for second
one.
Total resistance = sum of
resistances of resistors. PHY 101 Lecture #9
Electrical circuits
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Numerical example
If each resistor has R = 100 , total resistance is
200 .
If batterys V = 4.6 V,
I = V/R = 4.6 V / 200 = 23 mA.
Current through each resistor is 23 mA, and this
determines voltage drop across each resistor.
V = I R = 0.023 A * 100 = 2.3 V.
Total voltage drop across both resistors = 4.6 V,
matching battery. OK. PHY 101 Lecture #9
Electrical circuits
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Intuition about voltage,
from study of series connection
Voltage is a kind of electrical height in a
circuit.
Related to electric potential energy of a charged
object, just as height is related to gravitational
potential energy of a mass.
Series connection is called a voltage divider,
since part of voltage drop shows up across
each resistor. PHY 101 Lecture #9
Electrical circuits
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Parallel connection of
two resistors
Two resistors connected
side by side.
Same voltage across one is
voltage across other.
(Connected by wires.)
Current from battery splits
between two paths --
one path through each
resistor. PHY 101 Lecture #9
Electrical circuits
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Current in parallel connection of
two resistors Current through one resistor
plus current through other
resistor equals total current out
of battery.
Current through one resistor
equals V/R.
Total resistance of parallel
combination of two equal
resistors is R/2.