Series and Parallel Circuits Chapter 23 Series and Parallel Circuits

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

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.

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

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

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

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

Example Voltage drops in series circuit 8 8

Example Mathematical analysis of series circuit 9 9

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

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

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

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

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 + I3 + ... 14

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

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!

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

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.

Check Your Understanding Mathematical Analysis of Parallel Circuits 19

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. 1/3 b. 1/2 c. 2/3 d. the same as e. 1.5 times f. twice g. three times h. four times 20

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

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.

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.

Example

Example

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

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