Lesson 5: Parallel DC Circuits and Kirchhoffs Current Law (KCL) (Chapter 6)

1. Lesson 5: Parallel DC Circuits and Kirchhoffs Current Law (KCL)(Chapter 6)

2. Learning Objectives • Restate the definition of a node and demonstrate how to measure voltage and current in parallel circuits. • Solve for total circuit resistance of a parallel circuit. • State and apply KCL in the analysis of simple parallel circuits. • Demonstrate how to calculate the total parallel resistance given various resistors connected in parallel. • Evaluate why homes, businesses and ships are commonly wired in parallel rather than series. • Demonstrate how to calculate the total current and branch currents in a parallel circuit using the current divider equation. • Determine the net effect of parallel combining voltage sources. • Compute the power dissipated by each element in a parallel circuit, and calculate the total circuit power.

3. Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. 2-, 3-, and 2Aare in parallel Parallel Circuits

4. Parallel Circuits • Remember: nodes are connection points between components. • Notice each component has two terminals and each is connected to one of the nodes above.

5. Parallel Circuits • House circuits contain parallel circuits. • The parallel circuit will continue to operate even though one component may fail open – an advantage over the series circuit.

6. Parallel Circuits vs. Series Circuits • In a series circuit, failure of a single components can disable all components in the circuit. • In a parallel circuit, failure of one component will still allow other components to operate. Series Circuit Parallel Circuit

7. Circuit Breaker Panel • Homes and ships are usually wired in parallel instead of series. • All components can operate at rated voltage independent of other loads when wired in parallel.

8. Series - Parallel Circuits • Circuits may contain a combination of series and parallel components.

9. Parallel Circuits • To analyze a particular circuit • First identify the node. • Next, label the nodes with a letter or number. • Then, identify types of connections.

10. Example Problem 1 (A||B) || (C+(D||F)+E) Determine which elements are connected in parallel and which are connected in series. (A+B)+ C||F+(D+E) A+ (B||C||D) A||B||C||D

11. Kirchhoff’s Current Law (KCL) • Kirchhoff’s Current Law states that the algebraic sum of the currents entering and leaving a node is equal to zero. • Currents entering a node are positive and those leaving a node are negative.

12. Kirchhoff’s Current Law (KCL) • KCL can also be stated as “the sum of currents entering a node is equal to the sum of currents leaving the node.”

13. Parallel vs. Series Current Flow • Understanding how fluid flows may help with your understanding of KCL. • When water flows in a pipe, the amount of water entering a point is equal to the amount that leaves that point. • However, it should be noted that more water flows down the pipe with the lowest resistance.

14. Four-node configuration Two-node configuration Kirchhoff’s Current Law (KCL) • In technology, the term node is commonly used to refer to a junction of two or more branches.

15. Kirchhoff’s Current Law (KCL) • Determine I3 and I5 using KCL. Therefore, at node a: And at node b:

16. Parallel Circuit Kirchhoff’s Current Law (KCL) • Determine Is using KCL.

17. Direction of Current • Assume a current direction and draw current arrows. • If this assumption is incorrect, calculations will show that the current has a negative sign. • Negative sign simply indicates that the current flows in the opposite direction to the arrow you drew.

18. Example Problem 2 Determine the magnitude and direction of each current:

19. Battery Cells Series vs Parallel Cells connected in parallel increases available current. Cells connected in series increases available voltage. Recall that voltages are additive (ET = E1+E2+…+EN) in series. However, in parallel circuits, voltages will be equal across the parallel elements.

20. Voltage Sources in Parallel • When two equal sources are connected in parallel • Each source supplies half the required current

21. Demonstrating the effect of placing two ideal supplies of the same voltage in parallel. Voltage Sources in Parallel

22. Voltage Sources in Parallel • Because the voltage is the same across parallel elements, voltage sources can be placed in parallel only if they have the same voltage. • The primary reason for placing two or more batteries or supplies in parallel is to increase the current rating above that of a single supply.

23. Voltage Sources in Parallel • Voltage sources with different potentials should never be connected in parallel. • Large currents can occur and cause damage.

24. Examining the impact of placing two lead-acid batteries of different terminal voltages in parallel. Voltage Sources in Parallel • If, for some reason, two batteries of different voltages are placed in parallel, both will become ineffective or damaged because the battery with the larger voltage will rapidly discharge through the battery with the smaller terminal voltage.

25. Determine the currents I2 and I3. Example Problem 3 Knowing that voltage is equal across parallel elements we can first find v1… Now solve for each parallel current:

26. Resistors in Parallel • For only two resistors connected in parallel, the equivalent resistance may be found by the product of the two values divided by the sum: • Often referred to as “product over the sum” formula.

27. Resistors in Parallel • For a circuit with 3 or more resistors:

28. Resistors in Parallel • Since voltage across all parallel elements in a circuit are the same (E = V1 = V2=V3):

29. Resistors in Parallel • Total resistance of any number of resistors in parallel:

30. Resistors in Parallel • Sometimes you can solve resistive problems involving parallel circuits through inspection. • Below are a few examples of how this can be done:

31. Current Divider Rule • Similar to the Voltage Divider Rule, we can use the Current Divider Rule to calculate current across a resistive element without knowing the voltage drop across that element:

32. Example Problem 4 First, find an equivalent resistance (RT): Use the current divider rule to determine all unknown currents: Now use CDR:

33. Analysis of Parallel Circuits • Voltage across all parallel branches is the same as the source voltage. • Determine current through each branch using Ohm’s Law. • Find the total current using Kirchhoff’s Current Law.

34. Example Problem 5 • Determine all unknown currents and total resistance. • Verify KCL for node a. I6 I5 First: understand your circuit: I4 I1 I3 I2 270V 2.7kΩ 4.3kΩ 5.6kΩ 3.9kΩ IS Next, find total current (IT): Now, find an equivalent resistance (RT): Finally, use CDR and find the individual currents (Ix):

35. Power Calculations • As before, to calculate the power dissipated by each resistor, use: VI, I2R, or V2/R. • Total power consumed is the sum of the individual powers: PT = P1 + P2 +…+PN

36. Example Problem 6 • Solve for indicated currents. • Determine power dissipated by each resistor. • Verify total power = sum of all power dissipated. Find an equivalent resistance (RT): I1 I2 I3 30V IS Next, find total current (IT): Finally, find Px: Now, use CDR and find Ix:

37. QUESTIONS?