Chapter 8
DC Circuits
• Objectives
– After completing this chapter, the student
should be able to:
• Solve for all unknown values, (current, voltage,
resistance, and power) in a series, parallel, or seriesparallel circuit.
• Understand the importance of voltage dividers.
• Design and solve for all unknown values in a
voltage divider circuit.
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• Series Circuits
– Provide only one path for current flow.
– Factors governing operation are:
• The same current flows through each component.
IT = IR1 = IR2 = IR3 … = IRn
• The total resistance in a series circuit is equal to the
sum of the individual resistances.
RT = R1 + R2 + R3 … + Rn
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• The total voltage across a series circuit is equal to
the sum of the individual voltage drops.
ET = ER1 + ER2 + ER3 … + ERn
• The voltage drop across a resistor in a series circuit
is proportional to the size of the resistor.
I = E/R
• The total power dissipated in a series circuit is equal
to the sum of the individual power dissipations.
PT = PR1 + PR2 + PR3 … + PRn
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• To solve for values in a circuit (in order):
– Find the total resistance.
– Determine the total circuit current.
– Determine the voltage drops and dissipation.
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• Parallel Circuits
– Circuits having more than one current path.
– Factors governing operation are:
• The same voltage exists across each branch of the
parallel circuit and is equal to that of the voltage
source.
ET = ER1 = ER2 = ER3 … = ERn
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• The current through each branch of a parallel circuit
is inversely proportional to the amount of resistance
of the branch.
I = E/R
• The total current in a parallel circuit is the sum of
the individual branch currents.
IT = IR1 + IR2 + IR3 … + IRn
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• The reciprocal of the total resistance in a parallel
circuit is equal to the sum of the reciprocals of the
individual resistances.
1/RT = 1/R1 + 1/R2 + 1/R3 . . . + 1/Rn
• The total power consumed in a parallel circuit is
equal to the sum of the power consumed by the
individual resistors.
PT = PR1 + PR2 + PR3 … + PRn
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• Series-Parallel Circuits
– Circuits that consist of both series and parallel
circuits.
– To solve most series-parallel circuits, simply
apply laws and rules to each type.
• Series formulas are applied to series parts of the
circuit.
• Parallel formulas are applied to parallel parts of the
circuit.
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• Voltage Dividers
– Used to set a bias or operating point of various
active electronic components.
• Transistors
• Integrated circuits
– Used to divide a higher voltage to a lower
voltage.
– Often referred to as scaling.
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• Ohm’s Law
– The current through a circuit is directly
proportional to the voltage across the circuit
and inversely proportional to the resistance.
Current = voltage/resistance
I = E/R
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• Current Division
– Current is directly proportional to voltage
across the circuit.
• If voltage increases, current increases.
• If voltage decreases, current decreases.
– The voltage drop is equal to the percentage of
the dropping resistor to the sum of the dropping
network.
EDrop = ESource x RDrop / RTotal
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• In Summary
– A series circuit provides only one path for current flow.
– Series circuit formulas include:
•
•
•
•
•
IT = IR1 = IR2 = IR3 … = IRn
RT = R1 + R2 + R3 … + Rn
ET = ER1 + ER2 + ER3 … + ERn
I = E/R
PT = PR1 + PR2 + PR3 … + PRn
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– A parallel circuit provides more than one path
for current flow.
– Parallel circuit formulas include:
•
•
•
•
•
IT = IR1 + IR2 + IR3 … + IRn
1/RT = 1/R1 + 1/R2 + 1/R3 . . . + 1/Rn
ET = ER1 = ER2 = ER3 … = ERn
I = E/R
PT = PR1 + PR2 + PR3 … + PRn
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– Series-parallel circuits are solved by using
series formulas for the series parts of the circuit
and parallel formulas for the parallel parts of
the circuit.
– Voltage dividers
– Current division
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