1. Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2002 The McGraw-Hill Companies Grob Schultz

2. Basic Electronics Ninth Edition Basic Electronics Ninth Edition ©2003 The McGraw-Hill Companies 5 CHAPTER Parallel Circuits

3. Topics Covered in Chapter 5  Voltage and Current in parallel circuits  Kirchhoff’s current law  Resistance and conductance  Total power  Analyzing circuits  Troubleshooting

4. Characteristics of a Parallel Circuit Voltage is the same across each branch of the circuit. The total current is equal to the sum of the individual branch currents. The equivalent resistance (R EQ ) is less than the smallest branch resistance. Total power is equal to the sum of the power dissipated by each resistance.

5. V is constant. Voltage is the same everywhere in a parallel circuit. VVVV V Note: a group of components connected in parallel can be called a bank.

6. I1I1 V I2I2 I3I3 I4I4 ITIT ITIT The total current is equal to the sum of the branch currents. This is known as Kirchhoff’s current law (KCL). I T = I 1 + I 2 + I 3 + I 4

7. V ITIT Since the total current is the largest, the equivalent resistance must be smaller than the smallest branch resistance. R EQ < 10  10  20  40 

8. P1P1 V The total power is equal to the sum of the individual powers. P T = P 1 + P 2 + P 3 + P 4 P2P2 P3P3 P4P4

9. Voltage Formulas Parallel Circuits Total voltage is equal to each of the individual branch voltages: VVVV T  123  etc. V T = I T R EQ Total voltage is equal to total current times equivalent resistance:

10. Resistance Formulas Parallel Circuits The inverse of equivalent resistance is equal to the sum of inverses of the individual branch resistances: 1 R EQ 1 R1R1 1 R2R2 1 R3R3 = +++ …+ etc. R EQ = VTVT ITIT Equivalent resistance is equal to total voltage divided by the circuit current:

11. Determining the Equivalent Resistance V 10  20  40  1 R EQ 1 R1R1 1 R2R2 1 R3R3 1 R4R4 =+++ 1 1 20 1 10 1 40 1 =+++ = 0.2 R EQ = 5 

12. Special Case: Equal Value Resistors V 40  R EQ = 10  Divide the resistor value by the number of resistors.

13. Two Resistors: Alternate Formula V 10  40  R EQ = 8  R 1 x R 2 R 1 + R 2 R EQ = 40 x 10 40 + 10 =

14. Current Formulas Parallel Circuits Total current is equal to the sum of the individual branch currents: IIII T  123  etc. R EQ VTVT I T = Total current is equal to total voltage divided by equivalent resistance:

15. Determining the Currents 8 V 10  20  40  1234 I 1 = 8 V 20  = 0.4 A I 2 = 8 V 10  = 0.8 A I 3 = 8 V 40  = 0.2 A I 4 = 8 V 40  = 0.2 A I T = 0.4 + 0.8 + 0.2 + 0.2 = 1.6 A Check:I T = VTVT R EQ 8 V 5  = = 1.6 A

16. Total Power Parallel Circuits Total power is equal to the sum of the power dissipated by the individual resistances of the parallel branches: PPPP T  123  etc.PVI TTT  Total power is equal to total voltage times total current:

17. Determining Power 8 V 10  20  40  1234 P 1 = 8282 20  = 3.2 W P T = 3.2 + 6.4 + 1.6 + 1.6 = 12.8 W Check:P T = V T x I T = 8 x 1.6 = 12.8 W P 2 = 10  = 6.4 W 8282 P 3 = 40  = 1.6 W 8282 P 4 = 40  = 1.6 W 8282

18. Conductance in Parallel Circuits Conductance (G) is equal to 1/R. Total (equivalent) conductance of a parallel circuit is given by: G EQ = G 1 + G 2 + G 3 +…+ etc. G T = G 1 + G 2 + G 3 +…+ etc. or

19. Determining Conductance 8 V 10  20  40  1234 G 1 = 1 20  = 0.05 S G EQ = 0.05 + 0.1 + 0.025 + 0.025 = 0.2 S G 2 = 10  = 0.1 S 1 G 3 = 40  = 0.025 S 1 G 4 = 40  = 0.025 S 1

20. Open Circuit Parallel Circuit An open circuit in one branch results in no current through that branch. An open circuit in one branch has no effect on other branches.

21. An Open in a Parallel Circuit The other branches are not affected. (However, the total current is smaller.)

22. Connections sometimes fail.

23. Short Circuit Parallel Circuit A short circuit has zero resistance, resulting in excessive current in the shorted branch. A shorted branch shorts the entire circuit. Current does not flow in other branches that are not shorted.

24. A Short in a Parallel Circuit The other branches are shut down. (The total current is high).