1 AGBell – EECT by Andrew G. Bell (260) Lecture 5

2 AGBell – EECT CHAPTER 5 Parallel Circuits

3 AGBell – EECT Parallel Circuit Characteristics 1.There are two or more paths for current flow 2.The voltage is the same across all parallel branches

4 AGBell – EECT A Practical Example

5 AGBell – EECT Parallel Circuit Nodes Two types of nodes or connections: –Dividing Node: A junction where current enters by one connection but leaves by two or more connections –Summing Connection: A junction where current enters a junction by two or more connections but leaves via one

6 AGBell – EECT Parallel Circuit Nodes (cont.)

7 AGBell – EECT Parallel Circuit Current All branch currents are supplied by the power supply. Current leaving the (–) terminal is the same current entering the (+) terminal. This is referred to as total current (I T ). The total current equals the sum of the branch currents.

8 AGBell – EECT Parallel Circuit Current (cont.) Since the total current is equal to the current supplied by the source, the total current can be stated as: I T = I R1 + I R2 … + I Rn

9 AGBell – EECT Kirchhoff’s Current Law Kirchhoff’s current law states that the sum of the currents entering a junction must be equal to the sum of the currents leaving the junction: I in = I out

10 AGBell – EECT AGBell – EECT 111 Current in a Parallel Circuit If the applied voltage (and, therefore, the voltage across each branch) and the branch resistance are known, the current through each branch can be found by using Ohm’s law. The branch with the least resistance has the most current.

11 AGBell – EECT AGBell – EECT 111 Total Resistance Ohm’s law method:

12 AGBell – EECT AGBell – EECT 111 Conductance Method

13 AGBell – EECT AGBell – EECT 111 Product-Over-The-Sum Method This works for a circuit with only two resistors in parallel:

14 AGBell – EECT AGBell – EECT 111 Equal Value Branches Where R x is the value of the branch resistance and N is the number of branches

15 AGBell – EECT AGBell – EECT 111 Reciprocal Method This works for a circuit with any number of resistors in parallel:

16 AGBell – EECT AGBell – EECT 111 Assumed Voltage Method 1.Assume a supply voltage (V T ) 2.Calculate all branch currents 3.Add branch currents to find I T 4.Find R T by applying Ohm’s law:

17 AGBell – EECT AGBell – EECT 111 Example

18 AGBell – EECT AGBell – EECT 111 Total Resistance Important Concept The total resistance of parallel circuits is always less than the smallest value branch resistance.

19 AGBell – EECT AGBell – EECT 111 Power in Parallel Circuits 1. Summation method P T = P R1 + P R2 … + P Rn 2. Ohm’s law method

20 AGBell – EECT AGBell – EECT 111 Opens in Parallel Circuits 1.If a branch opens, the current goes to zero in that branch. 2.If the total current decreases, the total resistance increases. 3.Branch voltage remains the same across the open branch and the other branches.

21 AGBell – EECT AGBell – EECT 111 A Practical Example

22 AGBell – EECT AGBell – EECT 111 Shorts in Parallel Circuits Remember: There are 0  across a short. The branch resistance goes to 0  ; thus, the total resistance goes to 0 . Since there are 0  across the branches, no voltage drop is developed. A protective device is required because current is maximized.

23 AGBell – EECT AGBell – EECT 111 Contrasting Series and Parallel Circuits SERIES I T is constant KVL is used V T = sum of drops R T = sum of resistors PARALLEL I T is the sum of I Rn KCL is used V T is constant R T is reciprocal of the sum of the reciprocals

24 AGBell – EECT AGBell – EECT 111 Voltage Sources in Parallel Sources are used in parallel to increase the amount of total current available. While V T remains the same, I T increases by the amount of each source.

25 AGBell – EECT AGBell – EECT 111 Current Dividers in a Two-Branch Circuit

26 AGBell – EECT AGBell – EECT 111 Current Dividers in a Two-Branch Circuit (cont.)

27 AGBell – EECT AGBell – EECT 111 Current Dividers in a Two-Branch Circuit (cont.)