Series Circuits
2 February 2005
Series Circuits
Objective
• At the conclusion of this presentation the student will
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Identify a series circuit
Apply Ohm’s law in series circuits
Determine and identify ground in a circuit
Determine total series resistance
Determine the current in a series circuit
Determine the total effect of voltage sources in series
Apply Kirchhoff’s voltage law
Use a series circuit as a voltage divider
Determine power in a series circuit
Apply the proper prefix for units of measurement
2 February 2005
Professor Andrew H. Andersen
Series Circuits
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Series Circuits
2 February 2005
Series Circuit Characteristics
1.
The current is the same everywhere in the circuit.
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2.
Each component has an individual Ohm's law Voltage Drop.
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3.
5.
This means that I can calculate the voltage using Ohm's Law if I know the
current through the component and the resistance.
Kirchoff's Voltage Law (KVL) applies.
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4.
This means that wherever I try to measure the current, I will obtain the same
reading.
This means that the sum of all the voltage sources is equal to the sum of all
the voltage drops or
– VS = V1 + V2 + V3 + . . . + VN
The total resistance in the circuit is equal to the sum of the individual
resistances.
– RT = R1 + R2 + R3 + . . . + RN
The sum of the power supplied by the source is equal to the sum of the
power dissipated in the components.
– PT = P1 + P2 + P3 + . . . + PN
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Current in a Series Circuit
• The current in a series circuit is the same through all
points
• The current through each resistor in a series circuit is the same
as the current through all the other resistors that are in series
with it
• Current entering any point in a series circuit is the same as the
current leaving that point
2 February 2005
Professor Andrew H. Andersen
Series Circuits
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Series Circuits
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Current in a Series Circuit
Current in a series circuit is the same everywhere
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Measuring Current in a Series Circuit
In a series circuit the location of the ammeter does not
matter
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Professor Andrew H. Andersen
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Series Circuits
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Series Resistance Formula
• Regardless of the number of individual resistors connected in
series, the total resistance of a series circuit is the sum of each
of the individual values
RT = R1 + R2 + R3 + . . . + RN
• The total resistance will always be larger than the largest
individual resistor
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Total Series Resistance
• The total resistance of a series circuit is equal to the sum of the resistances
of each individual series resistor
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Professor Andrew H. Andersen
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Series Circuits
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Resistors in Series
• A series circuit provides only one path for current between two points so
that the current is the same through each series resistor
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Series Connected Resistance
RAB = R1 + R2
RAB = R1 + R2 + R3
RAB = R1 + R2 + R3 + R4
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Professor Andrew H. Andersen
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Series Circuits
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Total Series Resistance
RT is not dependent on component order
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Determining the Resistance on a Printed Circuit
Board
Trace the path from one end to the other and draw it on paper as you go
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Professor Andrew H. Andersen
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Series Circuits
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Resistors on a Protoboard
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Find R4
RT = R1 + R2 + R3 + R4
R4 = RT - R1 - R2 - R3
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Series Circuits
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Find R4
R4 = RT - R1 - R2 - R3
R4 = 146kΩ – 10kΩ – 33kΩ – 47kΩ
56kΩ
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Ohm’s Law in Series Circuits
• Current through one of the series resistors is the same as the current
through each of the other resistors and is the total current
• If you know the total voltage and the total resistance, you can determine
the current by using:
I=
VT
RT
• If you know the voltage drop across one of the series resistors, you can
determine the current by using any of the following:
I=
2 February 2005
Professor Andrew H. Andersen
VR1
VR2
VR3
VRN
=
=
=
R1
R2
R3
RN
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Ohm’s Law in Series Circuits
• If you know the total current, you can find the voltage drop
across any of the series resistors by using:
VR= I R
• The polarity of a voltage drop across a resistor is positive at
the end of the resistor that is closest to the positive terminal of
the voltage source
• The direction of current (electron flow) through a resistor is
from the negative end of the resistor to the positive end
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Ohm’s Law in Series Circuits
• An open (an open switch or circuit failure) in a series circuit
prevents all current from flowing (R = 0Ω)
I = 0A
• In an open series circuit, there is zero voltage drop across each
series resistor
• The supply voltage appears across the open points in the
circuit
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Professor Andrew H. Andersen
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Series Circuits
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Sources Connected Series Aiding
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Sources Connected Series Opposing
VT = VS1 – VS2 + VS3
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Kirchhoff’s Voltage Law
• The algebraic sum of all voltages (both sources and drops)
around a closed path is zero
ΣV = 0
or
VS – V1 – V2 – V3 - … - Vn = 0
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Kirchhoff’s Voltage Law
• The algebraic sum of all the
voltage drops around a
single closed loop in a
circuit is equal to the total
source voltage in that loop
VS = V1 + V2 + V3 + … + Vn
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Professor Andrew H. Andersen
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KVL
∑V
SOURCES
= ∑ VDROPS
10V = 5.5V + 4.5V
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Voltage Divider
I =
I
V1
VS
=
R1 R1 + R2
⎛ R1 ⎞
V1 = VS ⎜
⎟
⎝ R1 + R2 ⎠
⎛ R2 ⎞
V2 = VS ⎜
⎟
⎝ R1 + R2 ⎠
RT = R1 + R2
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Voltage Divider
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Calculate V1 and V2
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Calculate V1 and V2
82Ω
⎛
⎞
V1 = 10V ⎜
⎟
⎝ 82Ω + 68Ω ⎠
V1 = 5.47V
68Ω
⎛
⎞
V2 = 10V ⎜
⎟
⎝ 82Ω + 68Ω ⎠
V2 = 4.53V
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Use the Voltage Divider to Calculate V1, V2, and V3
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Use the Voltage Divider to Calculate V1, V2, and V3
⎛ 100Ω ⎞
V1 = 100V ⎜
⎟
⎝ 1000Ω ⎠
V1 = 10V
⎛ 220Ω ⎞
V2 = 100V ⎜
⎟
⎝ 1000Ω ⎠
V2 = 22V
⎛ 680Ω ⎞
V3 = 100V ⎜
⎟
⎝ 1000Ω ⎠
V3 = 68V
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Double Subscript Notation
Node Referenced
VAB
VAC
VBC
VCD
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Double Subscript Notation
Ground Referenced
VA
VB
VC
VD = 0V
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Calculate the Voltage Drops
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Power in a Series Circuit
• The total amount of power in a series resistive circuit is equal
to the sum of the powers in each resistor in series
PS = P1 + P2 + P3 + . . . + PN
VS I = V1 I + V2 I + V3 I + . . . + VN I
I2 RT = I2 R1 + I2 R2 + I2 R3 + . . . + I2 RN
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