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Parts of An Electric Circuit
• Recall: a circuit is a closed path
• Electric circuit: closed path that
flowing charge follows
• Constructing an electric circuit:
• Three key components needed:
• “Source”: a source of voltage
or current
• Component: a device that
requires electrical energy
• Connectors: something to
connect source to component
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Circuit Diagrams
• Circuit diagram: standardized
method of illustrating the parts
of a circuit
• Components, sources have
specific symbols
• Many components– what we’ll
use is the tip of the iceberg
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Circuit Sources
+
Negative end
Positive end
• Battery
• Provides potential difference for
circuit
• Electrons will flow from high
voltage to low voltage in circuit
Circuit Components
• Switch
• Controls path of current
within circuit
• On: ends of switch
connected, closes circuit
• Off: ends of switch not
connected, circuit open
Circuit Components
• Resistor
• Creates resistance in circuit
• Serve to reduce amount of
voltage remaining in circuit
• Causes energy to be released
from it– often thermal energy
• Example: incandescent light
bulb
Circuit Components
• Rheostat/Potentiometer
• Variable resistor: can change
its resistance
As You Come In…
• Find the voltage drop in this part of a circuit:
5.0 Ω
0.15 A
Circuit Components
• Capacitor
• Stores charge in the circuit
• Acts like temporary battery
• Builds up charge when
connected to source until
full
• Discharges charge when
disconnected from source
until empty
Circuit Components
• Inductor
• Resists changes in current
• If connected to source,
keeps current from
flowing for a while
• If disconnected from
source, keeps current
flowing for a while
(how???)
Circuit Components
• Ammeter
• Measures current running
through part of circuit
A
Circuit Components
• Voltmeter
• Measures voltage running
through part of circuit
V
Circuit Components
• Generic Device
• Appliance or general
electrical device that is part
of circuit
Name
Circuit Connectors
Node
No node
• Conductor/wire
• Connects sources, components
• Assumed to have negligible
resistance
• Junctions
• Sometimes connectors cross
paths or intersect
• Node: conductors connect
• No node: conductors do not
connect
Circuit Connectors
• Ground
• Connects circuit to “ground”
• “Ground” has electrical potential
of 0 V
• Prevents short circuits– more on
those later!
• Given the following circuit diagram:
• Want to know I
• Magnitude of I is simple:
R=V/I
I = V / R= 0.50 A
• What about direction?
Electron flow notation:
electrons flow from (-) to (+)
of a voltage source
Current flowing CCW
+
1.5 V
-
3.0 Ω
Circuit Diagrams: Determining Current
I = 0.50 A
Circuit Diagrams: Series Circuits
1.5 V
R2 = 3.0 Ω
R3 = 1.0 Ω
R1 = 5.0 Ω
• Given the following circuit diagram:
• Resistors are in a series– one after
another along one path
• Called a “series circuit”
Circuit Diagrams: Series Circuits
1.5 V
R2 = 3.0 Ω
R3 = 1.0 Ω
R1 = 5.0 Ω
• What do we know about circuit?
• Only one path for electrons to
flow
• Current through each resistor
must be the same
• I1 = I2 = I3
• Voltage drop by end of path must
equal voltage of source
• V1 + V2 + V3 = Vtotal
Circuit Diagrams: Series Circuits
1.5 V
R2 = 3.0 Ω
R3 = 1.0 Ω
R1 = 5.0 Ω
• Resistors in Series:
• I1 = I2 = I3 = I
• V1 + V2 + V3 = Vtotal
• Since all the currents are the
same, can rewrite above as:
V1 V2 V3
Vtotal
• +
+
=
I
I
I
I
V
• Because R = , this simplifies to
I
R1 + R2 + R3 = Rtotal
1.5 V
Rtotal = 9.0 Ω
Circuit Diagrams: Series Circuits
Equivalent Circuit
• Resistors in Series:
• I1 = I2 = I3 = I
• V1 + V2 + V3 = Vtotal
• Since all the currents are the
same, can rewrite above as:
V1 V2 V3
Vtotal
• +
+
=
I
I
I
I
V
• Because R = , this simplifies to
I
R1 + R2 + R3 = Rtotal
1.5 V
Rtotal = 9.0 Ω
Circuit Diagrams: Series Circuits
Equivalent Circuit
• Resistors in Series:
• I1 = I2 = I3 = I
• V1 + V2 + V3 = Vtotal
• Since all the currents are the
same, can rewrite above as:
V1 V2 V3
Vtotal
• +
+
=
I
I
I
I
V
• Because R = , this simplifies to
I
R1 + R2 + R3 = Rtotal
Practice Problem: Series Circuit
6.0 V
R2 = ?
3.0 A
R1 = 1.5 Ω
• Given the following circuit diagram,
what is the resistance of R2?
• R1 + R2 = Rtotal
Vtotal 6.0 V
=
= 2.0 Ω
• Rtotal =
3.0
A
I
• 1.5 Ω + R2 = 2.0 Ω
So R2 = 0.5 Ω
About Series Circuits
1.5 V
R2 = 3.0 Ω
R3 = 1.0 Ω
R1 = 5.0 Ω
• Advantages:
• Easy to set up (cheap)
• Batteries in series: voltages additive,
increases current
• Less connectors needed
• Disadvantages:
• Voltage divided between components–
more components, less voltage for each
• One path for current– if one
component fails, circuit fails
• Resistance increases– decreases
current within circuit
Circuit Diagrams: Parallel Circuits
• Given the following circuit diagram:
• Resistors along multiple, different,
parallel paths
• Called a “parallel circuit”
R1 = 5.0 Ω
1.5 V
R2 = 3.0 Ω
R3 = 1.0 Ω
Circuit Diagrams: Parallel Circuits
• What do we know about circuit?
• Multiple paths for e- to flow
• Total current of circuit equal to
current through each resistor
• I1 + I2 + I3 = Itotal
• Voltage drop the same across
1.5
V
each resistor– equals voltage of
source
• V1 = V2 = V3 = Vtotal
R1 = 5.0 Ω
R2 = 3.0 Ω
R3 = 1.0 Ω
Circuit Diagrams: Parallel Circuits
• Resistors in Parallel:
• V1 = V2 = V3 = V
• I1 + I2 + I3 = Itotal
• Since all the voltages are the
same, can rewrite above as:
I1 I2 I3
Itotal
• + + =
1.5
V
V
V
V
V
V
1 I
• Since R = , that means = ; thus,
I
R V
1
1
1
1
+
+
=
R1 R2 R3
Rtotal
R1 = 5.0 Ω
R2 = 3.0 Ω
R3 = 1.0 Ω
Circuit Diagrams: Parallel Circuits
• Resistors in Parallel:
• V1 = V2 = V3 = V
• I1 + I2 + I3 = Itotal
• Since all the voltages are the
same, can rewrite above as:
I1 I2 I3
Itotal
• + + =
1.5
V
V
V
V
V
V
1 I
• Since R = , that means = ; thus,
I
R V
1
1
1
1
+
+
=
R1 R2 R3
Rtotal
Rtotal = 1.8 Ω
Equivalent Circuit
Practice Problem: Parallel Circuit
• Given the following circuit diagram, what
would be the reading on the ammeter?
1
1
1
1
• +
+
=
R1 R2 R3
Rtotal
1
1
1
1
•
+
+
=
15 Ω 5.0 Ω 7.5 Ω
Rtotal
1
1
1
1
• 0.067 + 0.20 + 0.13 =
Ω
Ω Rtotal 6.0 V
Ω
1
1
= 0.40 , therefore Rtotal = 2.5 Ω
Rtotal
Ω
• I = V / Rtotal = 6.0 V / 2.5 Ω = 2.4 A
???
R1 = 15 Ω
R2 = 5.0 Ω
R3 = 7.5 Ω
About Parallel Circuits
• Advantages:
• Voltage the same across each component
• Total resistance decreases compared to
each component’s resistance
• Batteries in parallel make batteries last
longer
• Multiple paths for current– can be
redirected if one part of circuit fails 1.5
• Disadvantages:
• More connectors needed
• Batteries in parallel do not add to the
voltage of the circuit
R1 = 5.0 Ω
V
R2 = 3.0 Ω
R3 = 1.0 Ω
Circuit Diagrams: More About Series Circuits
1.5 V
C2 = 0.8 F
C3 = 0.4 F
C1 = 1.2 F
• Capacitors in Series:
• Recall: V1 + V2 + V3 = Vtotal for series
circuit
• Capacitors in series act like one big
capacitor
1.5 V
Ctotal = ???
Circuit Diagrams: More About Series Circuits
Equivalent Circuit
• Capacitors in Series:
• Recall: V1 + V2 + V3 = Vtotal for series
circuit
• Capacitors in series act like one big
capacitor– one amount of charge
(Q)
V1 V2 V3
Vtotal
• +
+
=
Q
Q
Q
Q
V
1 Q
• Since C = , that means = ; thus,
Q
C V
1
1
1
1
+
+
=
C1 C2 C3
Ctotal
1.5 V
Ctotal = 0.2 F
Circuit Diagrams: More About Series Circuits
Equivalent Circuit
• Capacitors in Series:
• Recall: V1 + V2 + V3 = Vtotal for series
circuit
• Capacitors in series act like one big
capacitor– one amount of charge
(Q)
V1 V2 V3
Vtotal
• +
+
=
Q
Q
Q
Q
V
1 Q
• Since C = , that means = ; thus,
Q
C V
1
1
1
1
+
+
=
C1 C2 C3
Ctotal
Circuit Diagrams: More About Parallel Circuits
• Capacitors in Parallel:
• Recall: V1 = V2 = V3 = V for parallel
circuit
• Capacitors in parallel are
independent of one another– each
contain their own charge
• Q1 + Q2 + Q3 = Qtotal
1.5 V
Q1 Q2 Q3
Qtotal
•
+
+
=
V
V
V
V
Q
• Because C = , this simplifies to
V
• C1 + C2 + C3 = Ctotal
C1 = 1.2 F
C2 = 0.8 F
C3 = 0.4 F
Circuit Diagrams: More About Parallel Circuits
• Capacitors in Parallel:
• Recall: V1 = V2 = V3 = V for parallel
circuit
• Capacitors in parallel are
independent of one another– each
contain their own charge
• Q1 + Q2 + Q3 = Qtotal
1.5 V
Q1 Q2 Q3
Qtotal
•
+
+
=
V
V
V
V
Q
• Because C = , this simplifies to
V
• C1 + C2 + C3 = Ctotal
Ctotal = 2.4 F
Equivalent Circuit
Circuits in Both Series and Parallel
• Many circuits utilize both series
and parallel circuit properties
within a circuit
• Case in point:
• How do you find the
equivalent resistance of this
circuit?
• Recommend: drawing
equivalent circuits
Equivalent Circuits
• Strategy: equivalent circuits
• Pick out parts that are
exclusively in series or in
parallel
• Simplify that part of circuit
• Repeat as needed until only
one equivalent circuit
component remains
• Question: What part should
be simplified first for this
problem?
Equivalent Circuits
• Step 1: Parallel Circuit
1
1
1
1
• +
+
=
R2 R3 R4
Reqv
1
1
1
1
•
+
+
=
1.5 Ω 1.5 Ω 1.5 Ω
Reqv
3
1
•
=
1.5 Ω
Reqv
1.5 Ω
• Reqv =
= 0.5 Ω
3
Equivalent Circuits
• Step 1: Parallel Circuit
1
1
1
1
• +
+
=
R1 R2 R3
Reqv
1
1
1
1
•
+
+
=
1.5 Ω 1.5 Ω 1.5 Ω
Reqv
3
1
•
=
1.5 Ω
Reqv
1.5 Ω
• Reqv =
= 0.5 Ω
3
• So what’s the next step?
Equivalent Circuits
• Step 2: Series Circuit
• R1 + Reqv + R5 = Rtotal
• 1.0 Ω + 0.5 Ω + 3.5 Ω = Rtotal
• 5.0 Ω = Rtotal
Equivalent Circuits
• Step 2: Series Circuit
• R1 + Reqv + R5 = Rtotal
• 1.0 Ω + 0.5 Ω + 3.5 Ω = Rtotal
• 5.0 Ω = Rtotal
Equivalent Circuits
• Try this one on your own!
Step 3
Step 2
Step 1
As You Come In…
• How should a voltmeter be
inserted into a circuit?
Parallel: V equal
for both branches
• How should an ammeter be
inserted into a circuit?
Very high R so very
little current comes
through
V
As You Come In…
Very high R so very
little current comes
through
• How should a voltmeter be
inserted into a circuit?
V
Parallel: V equal
for both branches
• How should an ammeter be
inserted into a circuit?
Series: I equal since
along same path
A
Very small R so very
little voltage lost to
device