Chapter 8

DC Circuits

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• 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 series-parallel 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