Chapter 4
Series Circuits
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C.Y. Lee
Objectives
Identify a series circuit
Determine the current in a series circuit
Determine total series resistance
Apply Ohm’s law in series circuits
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
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Resistors in Series
A series circuit provides only one path for current
between two points
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Current in a Series Circuit
The current is the same through all points in a
series circuit
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Current in a Series Circuit
Current entering any point in a series circuit is the
same as the current leaving that point
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Current in a Series Circuit
Example: How much current does ammeter 1 and
ammeter 2 indicate, respectively ?
500
IA1 = IA2 = 100 V/500 Ω = 0.2 A
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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
RT = R1 + R2 + R3 + . . . + Rn
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Ohm’s Law in Series Circuits
If you know the total voltage and the total resistance,
you can determine the total current by using:
IT = VT/RT
Example: Find the current in below circuit
RT = 82 + 18 + 15 + 10
= 125 Ω
I = VT/RT
= 25/125 = 0.2 A
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Ohm’s Law in Series Circuits
If you know the voltage drop across one of the series
resistors, you can determine the current by using:
I = VR/R
Example: Find the current in below circuit
I = VR/R
= 2/10 = 0.2 A
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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 = ITR
Example: Find the voltage drop in R1 resistor
RT = 82 + 18 + 15 + 10
= 125 Ω
I = VT/RT
= 25/125 = 0.2 A
VR1 = 0.2 × 82 = 16.4 V
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Ohm’s Law in Series Circuits
−
+
16.4
25V
200
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Voltage Sources in Series
When two or more voltage sources are in series,
the total voltage is equal to the the algebraic sum
(including polarities of the sources) of the
individual source voltages
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Voltage Sources in Series
Example: Determine VS(tot) in below circuit
?V
VS(tot) = 25 V − 15 V = 10 V
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Kirchhoff’s Voltage Law (KVL)
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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Another Way to state
Kirchhoff’s Voltage Law
The algebraic sum of all
voltages (both sources
and drops) around a
closed path is zero
Loop
VS
VS = V1 + V2 + V3 + … + Vn
VS - V1 - V2 - V3 - … - Vn = 0
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Vn
V3
V2
V1
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Kirchhoff’s Voltage Law
Example: Determine the VS in below circuit
−
8V
+
−
16 V
+
+
32 V
+
−
24 V
−
VS = 32 + 24 + 16 + 8 + 8 = 88 V
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Voltage Dividers
Since each resistor has the same current, the voltage
drops are proportional to the resistance values
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Voltage-Divider Formula
The voltage drop Vx
across any resistor
or combination of
resistors in a series
circuit
RX
VX =
VS
RT
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Application of Voltage Dividers
A voltage divider used for volume control
2
3
1
1
2
3
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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
PT = P1 + P2 + . . . + Pn
PT = IVS
PT = I 2 RT
VS2
PT =
RT
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PT = (15)2/(10+12+56+22) = 2.25 W
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Circuit Ground
Voltage is relative
This reference point in a circuit is usually the
ground point
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Measuring Voltages with
Respect to Ground
(Negative ground)
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(Positive ground)
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Open Circuit
An open in a series circuit prevents current
When an open occurs in a series circuit, all of the
source voltage appears across the open
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A Short in a Series Circuit
The voltage across a shorted series component (or
circuit) is 0 volts
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Summary
Current is the same at all points in a series circuit
The total resistance between any two points in a
series circuit is equal to the sum of all resistors
connected in series between those two points
Voltage sources in series add algebraically
Kirchhoff’s voltage law (KVL): The sum of the
voltage drops equals the total source voltage
Alternative KVL: The algebraic sum of all the
voltages around a closed loop is zero
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Summary
A voltage divider is a series arrangement of
resistors
Ground is zero volts with respect to all points
referenced to it in the circuit
The voltage across an open series element equals
the source voltage
The voltage across a shorted series component is
0 volts
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