Series and Parallel Circuits Chapter 21 Series and Parallel Circuits

Explain What do you think which light bulb will light up?

If you have a 60 W and a 100 W bulbs. Predict which one is brighter.   If you have a 60 W and a 100 W bulbs. Predict which one is brighter. Connect the 60 W and a 100 W bulbs in series. Now which one will be brighter. Most students do not know what it means for a light bulb to be a “100 watt bulb.” The majority interpret this to mean that the bulb always dissipates 100 W of power.

Analyze the series circuit and calculate current, voltage and power dissipation for each bulb. This demonstration also provides a nice opportunity to emphasize that a given battery or power supply with constant voltage will not always provide the same current. How much current is drawn from the battery depends on the resistance in the circuit. It’s best to “overlook” the resistance change with temperature, although you might want to discuss this qualitatively. R60 W = 240 Ω R100 W = 144 Ω I60 W= I100 W = 0.31 A P60 W = 23 W P100 W = 14 W

Series circuits When all the devices are connected end to end are said to be in series, 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

  Resistors in Series

Resistors in Series Resistors can be replaced by a single equivalent resistance without changing the current in the circuit.

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

RESISTORS IN SERIES

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

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. 16

Parallel circuits   17

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). 22

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? The current at Y is greater than the current at Q. The current at Y is greater than the current at P. The current at Y is greater than the current at Z. The current at P is greater than the current at Q. The current at Q is greater than the current at P. The current is the same at all locations.

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? The current at Y is greater than the current at Q. The current at Y is greater than the current at P. The current at Y is greater than the current at Z. The current at P is greater than the current at Q. The current at Q is greater than the current at P. The current is the same at all locations.

Check Your Understanding Mathematical Analysis of Parallel Circuits 25

Check Your Understanding A 12-V battery , a 12-ohm resistor and a 4-ohm resistor are connected as shown below. 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 26

Check Your Understanding A 12-V battery , a 12-ohm resistor and a 4-ohm resistor are connected as shown below. 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 27

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.

Resistors in Series and Parallel If a circuit is more complex, start with combinations of resistors that are either purely in series or in parallel. Replace these with their equivalent resistances; as you go on you will be able to replace more and more of them.

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?

Mystery Circuit Box2 How can you to predict the how the light bulbs are connected (schematic diagram) of the circuit.

Ammeters and Voltmeters An ammeter is a device for measuring current, and a voltmeter measures voltages. The current in the circuit must flow through the ammeter; therefore the ammeter should have as low a resistance as possible, for the least disturbance.

Ammeters and Voltmeters A voltmeter measures the potential drop between two points in a circuit. It therefore is connected in parallel; in order to minimize the effect on the circuit, it should have as large a resistance as possible.