"Relationship between Resistors in Series and Parallel Circuits" Ohm's Law PPT Courseware 4

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"Relationship between Resistors in Series and Parallel Circuits" Ohm's Law PPT Courseware 4

think

In actual circuits, there are usually several or more conductors forming a circuit. What is the total resistance after several conductors are connected in series? What is the relationship between total resistance and partial resistance?

When the electrician was repairing household appliances, he found that a 200-ohm resistor was burned out and needed to be replaced. However, he only had a few 50-ohm resistors on hand. Can he combine them to replace the 200-ohm resistor?

Apply Ohm's law to derive the relationship between the total resistance and the partial resistance of a series circuit

I1 = I2 = I string

U1 + U2 = U string

I1R1+I2R2=I string R string

R1+ R2= R string

Conclusion: The total resistance of a series circuit is equal to the sum of the series resistances.

The total resistance of a series circuit is greater than any one of its individual resistors.

Example 1: As shown in the picture on the right, the resistance of lamp L1 is 6Ω, and the resistance of lamp L2 is 14Ω. After the switch is closed, the ammeter indicates 0.3 A, and the voltage indication is ( )

A, 1.8V B, 4.2V C, 3V D, 6V

Solution: R string = R1 + R2 = 6Ω + 14Ω = 20Ω

The indication of the voltmeter: U=IR string=0.3A×20Ω=6V

Thinking: Why does the more resistors in series, the greater the total resistance?

The resistance of a conductor is related to its length. When the cross-sectional area and material are constant, the longer the length, the greater the resistance. Putting one resistor in series with another resistor is equivalent to increasing the length of the conductor, and their total resistance should be greater than any of the series resistors.

Apply Ohm's law to derive the relationship between the total resistance and the partial resistance of a parallel circuit

U1 = U2 = U and

I1 + I2 = I and

U1/R1+U2/R2=U union/R union

1/R1+1/R2=1/R and

Conclusion: The reciprocal of the total resistance of a parallel circuit is equal to the sum of the reciprocals of the parallel resistances.

The total resistance of a parallel circuit is less than any one of its resistors.

Example 2: As shown in the picture on the right, if a 3-ohm resistor and a 6-ohm resistor are connected in parallel, what is their equivalent resistance? If the voltage across the power supply is 3 volts, what is the current in the circuit?

Solution: Because 1/R=1/R1+1/R2=1/2

So R=2Ω

According to Ohm's law: I=U／R=1.5 A.

Thinking: Why does the more resistors connected in parallel, the smaller the total resistance?

The resistance of a conductor is related to the cross-sectional area. When the length and material are constant, the larger the cross-sectional area, the smaller the resistance. If a resistor is connected in parallel with another resistor, it is equivalent to increasing the cross-sectional area of ​​the conductor, and their total resistance should be less than any one of the partial resistances.

Summary of this section

Three relationships of series circuits:

Current relationship of series circuit: I1=I2=I string

Voltage relationship of series circuit: U1+U2=U total

The resistance relationship of the series circuit: R1+R2=Rtotal

Three relationships of parallel circuits:

Current relationship of parallel circuit: I1+I2=I parallel

Voltage relationship of parallel circuit: U1=U2=U total

Resistance relationship of parallel circuit: 1/Rtotal=1/R1+1/R2

Practice questions

1. An 8Ω resistor and a 2Ω resistor are connected in series. The equivalent resistance after series connection ( )

A. Less than 10Ω and greater than 6Ω B. Less than 8Ω and greater than 2Ω

C. Less than 2Ω D. Equal to 10Ω

2. A 10Ω resistor and a 0.1Ω resistor are connected in parallel. The total resistance after parallel connection ( )

A. Equal to 1Ω B. Less than 0.1Ω

C, equal to 10.1Ω D, greater than 0.1Ω, less than 10Ω

3. The resistance values ​​of the two resistors are 30Ω and 60Ω respectively. After connecting them in series, the total resistance is R1; after connecting them in parallel, the total resistance is R2, then R1:R2 equals ( )

A, 2:1 B, 1:2 C, 2:9 D, 9:2

4. In the circuit shown in the figure, the resistors R1 = 4Ω, R2 = 2Ω, and the power supply voltage remains unchanged. When switches S1 and S3 are open and S2 is closed, the ammeter indicates 0.5A; when switches S1 and S3 are closed and S2 is open, the ammeter indicates ____A.

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Update Time: 2024-07-22

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