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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. 2 • 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 3 • 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 4 5 • To solve for values in a circuit (in order): – Find the total resistance. – Determine the total circuit current. – Determine the voltage drops and dissipation. 6 • 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 7 • 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 8 • 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 9 10 • 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. 11 12 • 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. 13 • 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 14 • 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 15 • 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 16 – 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 17 – 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 18