Chapter 23Series 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:

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Example

• Voltage drops in series circuit

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Example

• Mathematical analysis of series circuit

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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

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• 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

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

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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.

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Parallel circuitsFacts

1. 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).

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Itotal = I1 + I2 + I3 + ...

...321 VVVVbattery

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!

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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).

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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.

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Check Your Understanding

• Mathematical Analysis of Parallel Circuits

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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

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Practice problems

• Page 626, # 15-19, and 24

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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.

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• 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.

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Combination circuit

Example

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Example

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Practice problems

• How many different ways can you connect 3 resistors?

Answer – 4 ways• How about 4 resistors?

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Practice problems

• Page 630, # 25-27, • Page 637, #67, 77, 81,

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