How To Calculate Total Resistance In A Series-parallel Circuit Pdf?

How to Calculate Total Resistance in a Series-Parallel Circuit

Series-parallel circuits are a common type of electrical circuit that can be found in a variety of everyday devices, such as radios, televisions, and computers. In this type of circuit, resistors are connected in either a series or parallel arrangement. The total resistance of a series-parallel circuit can be calculated using the following formula:

Rtotal = R1 + R2 + … + Rn

where:

• Rtotal is the total resistance of the circuit
• R1, R2, …, Rn are the resistances of the individual resistors

In this article, we will discuss how to calculate the total resistance of a series-parallel circuit in detail. We will also provide some examples to help you understand the concepts.

Series-Parallel Circuits

A series-parallel circuit is a circuit that contains both series and parallel connections of resistors. In a series connection, the resistors are connected end-to-end, so that the current flows through each resistor in turn. In a parallel connection, the resistors are connected across each other, so that the current can flow through any of the resistors.

The total resistance of a series-parallel circuit can be calculated by first finding the equivalent resistance of each series and parallel section of the circuit. The equivalent resistance of a series connection is the sum of the individual resistances, and the equivalent resistance of a parallel connection is the reciprocal of the sum of the reciprocals of the individual resistances.

Once you have found the equivalent resistance of each section of the circuit, you can add them together to find the total resistance of the circuit.

Examples

Let’s look at some examples of series-parallel circuits and how to calculate their total resistance.

Example 1

Consider the following series-parallel circuit:


In this circuit, there are two resistors in series (R1 and R2) and two resistors in parallel (R3 and R4). The total resistance of the series resistors is:

R1 + R2 = 10 + 20 = 30

The total resistance of the parallel resistors is:

1 / (1 / R3 + 1 / R4) = 1 / (1 / 5 + 1 / 10 ) = 2

The total resistance of the circuit is:

Rtotal = R1 + R2 + R3 + R4 = 30 + 2 = 32

Example 2

Now consider the following series-parallel circuit:


In this circuit, there are three resistors in series (R1, R2, and R3) and one resistor in parallel (R4). The total resistance of the series resistors is:

R1 + R2 + R3 = 10 + 20 + 30 = 60

The total resistance of the parallel resistor is:

1 / (1 / R4) = 1 / (1 / 40 ) = 40

The total resistance of the circuit is:

Rtotal = R1 + R2 + R3 + R4 = 60 + 40 = 100

Step	Formula	Example
1. Find the total resistance of the series resistors.	Rt = R1 + R2 + … + Rn	Rt = 10 + 20 + 30 = 60
2. Find the equivalent resistance of the parallel resistors.	1/Req = 1/R1 + 1/R2 + … + 1/Rn Req = 1/(1/R1 + 1/R2 + … + 1/Rn)	Req = 1/(1/10 + 1/20 + 1/30 ) = 5
3. Add the total resistance of the series resistors to the equivalent resistance of the parallel resistors to find the total resistance of the circuit.	Rt = Rs + Req	Rt = 60 + 5 = 65

How to Calculate Total Resistance in a Series-Parallel Circuit

A series-parallel circuit is a combination of series and parallel circuits. In a series circuit, the current is the same through all components, and the total resistance is the sum of the individual resistances. In a parallel circuit, the voltage is the same across all components, and the total resistance is less than the smallest individual resistance.

The total resistance of a series-parallel circuit can be calculated by using the following formula:

Rtotal = R1 + R2 + … + Rn

where R1, R2, …, Rn are the individual resistances of the components in the circuit.

Series Circuits

A series circuit is a circuit in which the components are connected in a single path. The current flows through all of the components in the circuit in the same direction.

The total resistance of a series circuit is the sum of the individual resistances of the components in the circuit. This can be calculated using the following formula:

Rtotal = R1 + R2 + … + Rn

where R1, R2, …, Rn are the individual resistances of the components in the circuit.

Example Problems

Problem 1

A series circuit contains three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms. What is the total resistance of the circuit?

Solution

The total resistance of the circuit is:

Rtotal = R1 + R2 + R3

Rtotal = 10 ohms + 20 ohms + 30 ohms

Rtotal = 60 ohms

Problem 2

A series circuit contains a 100-watt light bulb and a 200-watt light bulb. The voltage of the circuit is 120 volts. What is the total resistance of the circuit?

Solution

The total resistance of the circuit can be calculated using the following formula:

Rtotal = V2 / P

where V is the voltage of the circuit and P is the power of the light bulb.

Rtotal = (120 volts)2 / (100 watts + 200 watts)

Rtotal = (14400 volts2) / 300 watts

Rtotal = 48 ohms

Parallel Circuits

A parallel circuit is a circuit in which the components are connected in parallel paths. The voltage is the same across all of the components in the circuit, but the current can flow through any of the paths.

The total resistance of a parallel circuit is less than the smallest individual resistance of the components in the circuit. This can be calculated using the following formula:

1 / Rtotal = 1 / R1 + 1 / R2 + … + 1 / Rn

where R1, R2, …, Rn are the individual resistances of the components in the circuit.

Example Problems

Problem 1

A parallel circuit contains three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms. What is the total resistance of the circuit?

Solution

The total resistance of the circuit is:

1 / Rtotal = 1 / R1 + 1 / R2 + 1 / R3

1 / Rtotal = 1 / 10 ohms + 1 / 20 ohms + 1 / 30 ohms

1 / Rtotal = 3 / 60 ohms

Rtotal = 60 / 3 ohms

Rtotal = 20 ohms

Problem 2

A parallel circuit contains a 100-watt light bulb and a 200-watt light bulb. The voltage of the circuit is 120 volts. What is the total resistance of the circuit?

Solution

The total resistance of the circuit can be calculated using the following formula:

1 / Rtotal = 1 / R1 + 1 / R2

where R1 and R2 are the resistances of the light bulbs.

1 / Rtotal = 1 / 1

3. Combination Circuits

A combination circuit is a circuit that contains both series and parallel connections. To calculate the total resistance of a combination circuit, you must first find the equivalent resistance of each series and parallel section of the circuit. Then, you can add the equivalent resistances of the series and parallel sections to find the total resistance of the circuit.

Definition of a Combination Circuit

A combination circuit is a circuit that contains both series and parallel connections. In a series circuit, the current flows through all of the components in the same path. In a parallel circuit, the current flows through each of the components in separate paths.

Calculating the Total Resistance of a Combination Circuit

To calculate the total resistance of a combination circuit, you must first find the equivalent resistance of each series and parallel section of the circuit. Then, you can add the equivalent resistances of the series and parallel sections to find the total resistance of the circuit.

Finding the Equivalent Resistance of a Series Section

To find the equivalent resistance of a series section of a circuit, you add the resistances of the individual components in the section. For example, if you have a series section of three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms, the equivalent resistance of the section would be 10 + 20 + 30 = 60 ohms.

Finding the Equivalent Resistance of a Parallel Section

To find the equivalent resistance of a parallel section of a circuit, you divide the sum of the reciprocals of the individual resistances by the number of resistors in the section. For example, if you have a parallel section of three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms, the equivalent resistance of the section would be (1 / 10 + 1 / 20 + 1 / 30) = 6 / 50 = 10 / 13 ohms.

Adding the Equivalent Resistances

Once you have found the equivalent resistance of each series and parallel section of the circuit, you can add the equivalent resistances to find the total resistance of the circuit. For example, if you have a circuit with a series section with an equivalent resistance of 60 ohms and a parallel section with an equivalent resistance of 10 / 13 ohms, the total resistance of the circuit would be 60 + (10 / 13) = 66.67 ohms.

4. Tips and Tricks

How to Remember the Formulas for Calculating Total Resistance

There are a few different ways to remember the formulas for calculating total resistance. One way is to remember that the equivalent resistance of a series circuit is equal to the sum of the resistances of the individual components, and the equivalent resistance of a parallel circuit is equal to the reciprocal of the sum of the reciprocals of the individual resistances. Another way to remember the formulas is to use the following mnemonic devices:

• Series: Sum of Resistances
• Parallel: Peciprocal of Reciprocals

How to Troubleshoot Series-Parallel Circuits

If you are having trouble troubleshooting a series-parallel circuit, there are a few things you can check. First, make sure that you have identified all of the components in the circuit and that you know their values. Second, make sure that you have drawn a schematic diagram of the circuit. Third, use the formulas for calculating total resistance to find the total resistance of the circuit. Finally, use Ohm’s law to calculate the current and voltage in the circuit.

Additional Resources

• [The Physics Classroom: Series and Parallel Circuits](https://www.physicsclassroom.com/class/circuits/Lesson-2/Series-and-Parallel-Circuits)
• [Khan Academy: Series and Parallel Circuits](https://www.khanacademy.org/science/physics/circuits-and-electromagnetism/circuit-basics/a/series-and-parallel-circuits)
• [Electrical4U: Series and Parallel Circuits](https://www.electrical4u.com/series-and-parallel-circuits/)

In this article, you learned how to calculate the total resistance of a combination circuit. You also learned about the different

Q: What is a series-parallel circuit?

A series-parallel circuit is a circuit that contains both series and parallel connections. In a series connection, the current flows through each resistor in turn, while in a parallel connection, the current can flow through any of the resistors.

Q: How do you calculate the total resistance of a series-parallel circuit?

To calculate the total resistance of a series-parallel circuit, you can use the following formula:

Rtotal = R1 + R2 + … + Rn

where R1, R2, …, Rn are the resistances of the individual resistors in the circuit.

Q: What is the difference between a series circuit and a parallel circuit?

In a series circuit, the current flows through each resistor in turn, while in a parallel circuit, the current can flow through any of the resistors. This means that the total resistance of a series circuit is greater than the resistance of any individual resistor, while the total resistance of a parallel circuit is less than the resistance of any individual resistor.

Q: What are the advantages and disadvantages of series-parallel circuits?

Series-parallel circuits can be used to achieve a variety of different effects. For example, they can be used to increase or decrease the total resistance of a circuit, or to create a circuit that is more tolerant to damage. However, series-parallel circuits can also be more complex to design and troubleshoot than other types of circuits.

Q: How can I use a series-parallel circuit to increase the total resistance of a circuit?

To increase the total resistance of a circuit, you can connect the resistors in series. This will increase the total resistance of the circuit because the current will have to flow through each resistor in turn.

Q: How can I use a series-parallel circuit to decrease the total resistance of a circuit?

To decrease the total resistance of a circuit, you can connect the resistors in parallel. This will decrease the total resistance of the circuit because the current can flow through any of the resistors.

Q: What are some common applications of series-parallel circuits?

Series-parallel circuits are used in a variety of applications, including:

• Electrical circuits
• Electronic circuits
• Lighting circuits
• Power distribution systems
• Audio systems
• Security systems
• Communication systems

Q: Where can I learn more about series-parallel circuits?

You can learn more about series-parallel circuits by reading books, articles, and online resources. You can also find tutorials and videos on how to design and troubleshoot series-parallel circuits.

we have discussed how to calculate the total resistance in a series-parallel circuit. We first learned that in a series circuit, the total resistance is equal to the sum of the individual resistances. Then, we learned that in a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. Finally, we put these two concepts together to learn how to calculate the total resistance in a series-parallel circuit.

Here are the key takeaways from this discussion:

• In a series circuit, the total resistance is equal to the sum of the individual resistances.
• In a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.
• To calculate the total resistance in a series-parallel circuit, first find the total resistance of the series resistors and then the total resistance of the parallel resistors. Then, add these two resistances together to find the total resistance of the entire circuit.