1. Chapter 8 DC Circuits

2. 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.

3. 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

4. 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

6. To solve for values in a circuit (in order): • Find the total resistance. • Determine the total circuit current. • Determine the voltage drops and dissipation.

7. 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

8. 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

9. 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

11. 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.

13. 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.

14. 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

15. 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

16. 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

17. 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

18. 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