Transcript Series Circuits

Example Series Circuit
V1
V2
•What is the total resistance?
•What is the current, IT?
•What is the voltage across each resistor?
EGR 101
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Kirchhoff’s Voltage Law

Note, in the example on the
previous page,
Vs = V1 +V2
EGR 101
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Series Circuit Characteristics

Series circuits have the following
voltage characteristic:
VS  V1  V2  ...  Vn
where
VS = the source (or total supply) voltage
Vn = the voltage across the highest numbered
resistor in the circuit
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Voltage Relationships

Kirchhoff’s Voltage Law

The sum of the component voltages in a
series circuit must equal the net source
voltage
VS  V1  V2 ...  Vn

1840 – German Physicist, Gustav Kirchhoff
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Series Circuit Characteristics

Power Characteristics
PS  VS I S  P1  P2  ...  Pn  PT
where
PS = the source power
PT = the total power dissipated by the circuit
Pn = the power that is dissipated across the
highest numbered resistor in the
circuit
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Team Activity # 1: Refer to Figure
4.45(d) on p. 125 of textbook
Method 1:



Calculate the total resistance of the circuit, RT.
Calculate I using RT and Ohm’s Law.
Calculate the total power PT using Vs and I.
Method 2:



Calculate I using Ohm’s Law.
Calculate the voltage across each resistance, V1, V2,V3
& V4.
Calculate the power in each resistor P1, P2, P3 & P4.
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Comparison of Results

Questions:

Does the VT you computed in Method 2
equal Vs from Method 1?

Does the sum of P1, P2, P3 & P4 equal PT
from Method 1?
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Voltage Notations


Single subscript, VA
– indicates the voltage
is measured from the
specified point relative
to ground
A
+
_
+
Two subscripts, VAB
– indicates the voltage
is measured from the
first identified point to
the second
A
_
+ B
_
EGR 101
}
VA
}
}
VAB
V?
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Voltage Divider

The Voltage Divider Relationship
– Often used to analyze a portion of a
series circuit
A

Allows us to
determine
individual
voltages
R1
1k
Rest
of
Circuit
R2
1k
R3
1k
B
EGR 101
}
}
}
V1
V2
V3
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Voltage Divider Relation

For a series combination of N resistors with
Vs (VAB in previous slide) applied across
them, the voltage across Rn is:
Rn
Vn  Vs
RT
where
Rn = the resistor n of interest
Vn = the voltage across across Rn
RT = the total series resistance
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Team Activity # 2: Refer to
Figure 4.46(c) on p. 125 of textbook
1. Calculate the voltage across each resistor, R1,
R2, & R3 by the Voltage Divider Method.
2. What is the resistance from point A to ground?
3. Calculate the current through each resistor using
your results from step 1.
4. Calculate the current in the circuit based on Vs
and total resistance.
5. Do your results from steps 3 and 4 agree?
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The Potentiometer as a
Voltage Divider

Audio Amplifier Application
VB  ?
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Team Activity # 3: Refer to
Figure 4.39(b) on p. 122 of textbook

Solve problem 12.
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