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

2. Series Parallel Circuits
Basic Electronics
Ninth Edition 6
CHAPTER
Series Parallel Circuits
©2003 The McGraw-Hill Companies

3. Topics Covered in Chapter 6
Finding REQ for series-parallel resistances
Resistance strings in parallel and banks in series
Analysis of series-parallel circuits
The Wheatstone bridge
Opens and shorts in series-parallel circuits

4. Sections of Series-Parallel Circuits
Series components can be called a string.
Parallel components can be called a bank.
Series-parallel circuits combine strings and banks.
A string can have parallel sections.
A branch can have series sections.

5. A series
string V

6. Another
series
string V

7. The series strings are in parallel and act as branches. Series stringsV

8. There are three branches in this
circuit; sections 1 and 2 are series strings. 1 2 3 V

9. There are three series sections in this
circuit; sections 1 and 2 are banks. 1 2 3 V

10. Comparison of Series and Parallel Circuits Voltage and Current
Series Circuit
Current is the same in all components.
V across each series R is I ´ R.
Parallel Circuit
Voltage is the same across all branches.
I in each branch R is V/R.

11. I is constant
in this
section. V

12. I is
constant
in this
section. V

13. V is constant across the branches.

14. Determining Current Flow
IT = 2 A + 1 A + 2 A = 5 A IT
2 W
10 W I3
I3 =
20 V
5 W + 3 W + 2 W
= 2 A
10 W
3 W
20 V
I1 =
20 V
10 W
= 2 A I1 I2
I2 =
20 V
10 W + 10 W
= 1 A
10 W
5 W
REQ = VT IT =
20 V
5 A
= 4 W

15. Determining REQ Directly1 10 +
2 W 1 10 1 20 +
10 W
10 W
3 W
10 W
5 W 1
REQ =
= 0.25
REQ = 4 W

16. Comparison of Series and Parallel Circuits Resistance and Conductance
Series Circuit
RT = R1+R2+R3+…etc.
RT must be greater than the largest individual R.
Parallel Circuit
GT = G1+G2+G3+…etc.
GT must be more than the largest branch G.
REQ must be less than the smallest branch R.

17. Determine REQ for the banks, then for the entire circuit.
4 W
5 W
20 W
1 W
5 W
10 W
10 W
REQ = 4 W + 1 W + 5 W = 10 W

18. Determine the Total Current.
5 W
20 W
1 A
1 W
10 V
10 W
10 W
IT =
REQ VT =
10 V
10 W
= 1 A

19. Determine the Voltage Drops.
5 W
V = IR = 1V
V = IR = 1 A x 4 W = 4 V
4 V
20 W
1 A
1 W
10 V
V = IR = 1 A x 5 W = 5 V
5 V
10 W
10 W
Use Ohm’s Law, IT, and bank REQ to find the bank drops.
KVL check: 4 V + 1 V + 5 V = 10 V

20. Determine Bank Currents.
I(5 W) =
4 V
5 W
= 0.8 A
0.8 A
5 W
I(20 W) =
4 V
20 W
= 0.2 A
0.2 A
20 W
4 V
1 A
1 W
V = IR = 1V
10 V
5 V
10 W
10 W
KCL check: 0.8 A A = 1 A

21. Comparison of Series and Parallel Circuits Miscellaneous Notes
Series Circuit
Applied voltage is divided into IR voltage drops.
The largest IR drop is across the largest R.
Parallel Circuit
Main-line current is divided into branch currents.
The largest branch I is in the smallest branch R.

22. Wheatstone Bridge When R1/R2 = R3/R4 the bridge is balanced.
V = 0
When the bridge is balanced, V = 0. R4 R2
30 W
300 W
When R1/R2 = R3/R4 the bridge is balanced.

23. Using a Wheatstone Bridge to Measure an Unknown ResistanceRX R1 RX
= RS x R1 R2
V = 0 RS R2
3k W
RS is a standard resistor and is calibrated.
300 W
RS is adjusted to make V = 0.
The unknown resistor is 3 kW x (100/300) = 1 kW

24. An Open in a Series-Parallel Circuit
Normal current, drops, and power
dissipation in these two branches
V appears across the open V V

25. An Open in a Series-Parallel Circuit
Total current is smaller
Lower drops here (and less dissipation)
Higher drop here
Increased dissipation in the good resistor 2
3 & 4 V

26. A Short in a Series-Parallel Circuit2
The total current and total power increase.
Normal current, drops, and power dissipation in these two branches.
The drop and power increase here. 3 V

27. A Short in a Series-Parallel Circuit
Total current is larger.
Total power is larger.
Higher drops here (and more dissipation)
Zero drop here
Zero dissipation in the good resistor 3
4 & 5 V