1. Series and Parallel Circuits
Chapter 23
Series and Parallel Circuits

2. Series and parallel circuits
Calculate equivalent resistance
Calculate current and voltage drops in series and parallel circuits
Combination circuits

3. Explain Think about and explain how a flashlight is set up.
Explain how the brightness of a flashlight bulb would change if you could add more batteries.

4. Series circuits
When all the devices are connected using series connections, the circuit is referred to as a series circuit.
In a series circuit, each device is connected in a manner such that there is only one pathway

5. In series circuits, the same current flows through all of the components
The voltage across the components is the sum of the voltages across each component.
In a series circuit, every device must function for the circuit to be complete.
Resistors in Series

6. Resistors in Series
Resistors connected end to end are said to be in series.

7. Resistors in Series
The total resistance of resistors in series is equal to the sum of their individual resistances:

8. Example
Voltage drops in series circuit 8 8

9. Example
Mathematical analysis of series circuit 9 9

10. Example
Compare circuit X and Y below. Each is powered by a 12-volt battery. The voltage drop across the 12-ohm resistor in circuit Y is ____ the voltage drop across the single resistor in X.
a. smaller than
b. larger than
c. the same as 10 10

11. c. the same brightness in both circuits
A 12-V battery, a 12-ohm resistor and a light bulb are connected as shown in circuit X below. A 6-ohm resistor is added to the 12-ohm resistor and bulb to create circuit Y as shown. The bulb will appear ____.
a. dimmer in circuit X
b. dimmer in circuit Y
c. the same brightness in both circuits 11 11

12. Page 619, # 1-5 odds
Page 622, # 7, 10
Page 623, # 12, 14 12 12

13. Parallel circuits
When all the devices are connected using parallel connections, the circuit is referred to as a parallel circuit.
In a parallel circuit,
- each device is placed in its own separate branch.
- there are multiple pathways for charge flow. 13

14. Parallel circuits Facts
In parallel, all components have the same potential difference (voltage) across their ends.
2. The total current is the sum of the currents through the individual components. The current outside the branches is the same as the sum of the current in the individual branches.
This is called Kirchhoff's current law (KCL).
Itotal = I1 + I2 + I 14

15. Resistors in Series and Parallel
Resistors can again be replaced by a single equivalent resistance:

16. Resistors in Series and Parallel
Using the facts 1 and 2, we find:
Note that this equation gives you the inverse of the resistance, not the resistance itself!

17. Check Your Understanding
As more and more resistors are added in parallel to a circuit, the equivalent resistance of the circuit ____________ (increases, decreases) and the total current of the circuit ____________ (increases, decreases). 17

18. Check Your Understanding
Three identical light bulbs are connected to a D-cell as shown below. P, Q, X, Y and Z represent locations along the circuit. Which one of the following statements is true?
a. The current at Y is greater than the current at Q.
b. The current at Y is greater than the current at P.
c. The current at Y is greater than the current at Z.
d. The current at P is greater than the current at Q.
e. The current at Q is greater than the current at P.
f. The current is the same at all locations.

19. Check Your Understanding
Mathematical Analysis of Parallel Circuits 19

20. Check Your Understanding
A 12-V battery , a 12-ohm resistor and a 4-ohm resistor are connected as shown. The current in the 12-ohm resistor is ____ that in the 4-ohm resistor.
a. 1/ b. 1/2
c. 2/ d. the same as
e. 1.5 times f. twice
g. three times h. four times 20

21. Practice problems
Page 626, # 15-19, and 24 21

22. Combination circuit
A third type of circuit involves the dual use of series and parallel connections in a circuit; such circuits are referred to as compound circuits or combination circuits.

23. Combination circuit
The basic strategy for the analysis of combination circuits involves using the meaning of equivalent resistance for parallel branches to transform the combination circuit into a series circuit.

24. Example

25. Example

26. Practice problems How many different ways can you connect 3 resistors?
Answer – 4 ways
How about 4 resistors?

27. Practice problems
Page 630, # 25-27,
Page 637, #67, 77, 81,