Calculating the Maximum Resistance

Oct 13, 2025 by windailys.com 109 views

Introduction

When working with resistors, understanding how to connect them to achieve specific resistance values is crucial in various engineering applications. In this scenario, we are given four 100kΩ resistors and are tasked with connecting them to form a network with two terminals, ensuring that we do not create a short circuit or an open circuit. Our goal is to determine the ratio of the maximum to minimum resistance that we can realize.

Understanding Resistance

Before we dive into the problem, let's briefly review the concept of resistance. Resistance is a measure of the opposition to the flow of electric current through a conductor. It is measured in ohms (Ω) and is denoted by the symbol R. The total resistance of a circuit is the sum of the individual resistances of its components.

Connecting the Resistors

To maximize the resistance of the network, we need to connect the resistors in a way that creates the largest possible resistance. One way to achieve this is by connecting the resistors in series. When resistors are connected in series, the total resistance is the sum of the individual resistances.

R_total = R1 + R2 + R3 + R4

However, connecting the resistors in series will not give us the maximum possible resistance. To achieve this, we need to connect the resistors in a way that creates a voltage divider. A voltage divider is a circuit that reduces the voltage of a signal while keeping the current constant.

Voltage Divider Circuit

A voltage divider circuit consists of two or more resistors connected in series between a voltage source and ground. The output voltage of the circuit is proportional to the ratio of the resistances of the two resistors.

V_out = V_in * (R2 / (R1 + R2))

To maximize the resistance of the network, we can connect the four 100kΩ resistors in a voltage divider circuit with two terminals. One way to do this is by connecting two resistors in series and then connecting the other two resistors in series. The two series circuits are then connected in parallel.

R1 = 100kΩ
R2 = 100kΩ
R3 = 100kΩ
R4 = 100kΩ
R_total = (R1 + R2) || (R3 + R4)

Calculating the Maximum Resistance

To calculate the maximum resistance of the network, we need to calculate the total resistance of the two series circuits and then connect them in parallel.

R1_total = R1 + R2 = 200kΩ
R2_total = R3 + R4 = 200kΩ
R_total = R1_total || R2_total = 100kΩ

However, this is not the maximum possible resistance. To achieve this, we need to connect the resistors in a way that creates a voltage divider with the maximum possible resistance.

Calculating the Minimum Resistance

To calculate the minimum resistance of the network, we need to connect the resistors in a way that creates a short circuit. One way to do this is by connecting all four resistors in parallel.

R1 = 100kΩ
R2 = 100kΩ
R3 = 100kΩ
R4 = 100kΩ
R_total = R1 || R2 || R3 || R4 = 25kΩ

Calculating the Ratio of Maximum to Minimum Resistance

To calculate the ratio of the maximum to minimum resistance, we need to divide the maximum resistance by the minimum resistance.

R_max = 100kΩ
R_min = 25kΩ
ratio = R_max / R_min = 4

Conclusion

In conclusion, we have shown that the ratio of the maximum to minimum resistance that can be realized with four 100kΩ resistors is 4. This is achieved by connecting the resistors in a voltage divider circuit with two terminals. The maximum resistance is 100kΩ, and the minimum resistance is 25kΩ.

References

[1] "Resistors in Series and Parallel" by All About Circuits
[2] "Voltage Dividers" by Electronics Tutorials
[3] "Resistor Networks" by HyperPhysics

Q: What is the maximum resistance that can be realized with four 100kΩ resistors?

A: The maximum resistance that can be realized with four 100kΩ resistors is 100kΩ. This is achieved by connecting the resistors in a voltage divider circuit with two terminals.

Q: How do I connect the resistors to achieve the maximum resistance?

A: To connect the resistors to achieve the maximum resistance, you need to connect two resistors in series and then connect the other two resistors in series. The two series circuits are then connected in parallel.

Q: What is the minimum resistance that can be realized with four 100kΩ resistors?

A: The minimum resistance that can be realized with four 100kΩ resistors is 25kΩ. This is achieved by connecting all four resistors in parallel.

Q: How do I calculate the ratio of the maximum to minimum resistance?

A: To calculate the ratio of the maximum to minimum resistance, you need to divide the maximum resistance by the minimum resistance. In this case, the ratio is 4.

Q: What is the significance of the ratio of the maximum to minimum resistance?

A: The ratio of the maximum to minimum resistance is significant because it indicates the range of resistance values that can be achieved with the given resistors. In this case, the ratio of 4 indicates that the maximum resistance is four times the minimum resistance.

Q: Can I achieve a higher ratio of maximum to minimum resistance with more resistors?

A: Yes, you can achieve a higher ratio of maximum to minimum resistance with more resistors. However, the number of resistors required to achieve a specific ratio will depend on the individual resistance values and the desired ratio.

Q: What are some common applications of resistor networks?

A: Resistor networks have a wide range of applications, including:

Voltage dividers
Current dividers
Filter circuits
Amplifier circuits
Switching circuits

Q: How do I choose the right resistors for my circuit?

A: To choose the right resistors for your circuit, you need to consider the following factors:

The desired resistance value
The power rating of the resistors
The temperature coefficient of the resistors
The tolerance of the resistors

Q: What are some common mistakes to avoid when working with resistor networks?

A: Some common mistakes to avoid when working with resistor networks include:

Connecting resistors in parallel without considering the voltage drop across each resistor
Using resistors with different power ratings in the same circuit
Failing to consider the temperature coefficient of the resistors
Using resistors with high tolerance values in critical applications

Q: Where can I find more information about resistor networks?

A: You can find more information about resistor networks in various online resources, including:

Electronics textbooks
Online tutorials and courses
Manufacturer datasheets and application notes
Online forums and communities

Q: How do I troubleshoot resistor network problems?

A: To troubleshoot resistor network problems, you need to follow these steps:

Identify the symptoms of the problem
Measure the voltage and current across each resistor
Check the resistance values of each resistor
Verify that the resistors are connected correctly
Consult the datasheet and application notes for the resistors

Q: What are some common tools used to measure resistance?

A: Some common tools used to measure resistance include:

Multimeters
Ohmmeters
Resistance bridges
Digital multimeters

Q: How do I calibrate my multimeter to measure resistance accurately?

A: To calibrate your multimeter to measure resistance accurately, you need to follow these steps:

Consult the user manual for the multimeter
Use a known resistance value to calibrate the multimeter
Verify that the multimeter is reading the correct resistance value
Adjust the multimeter as necessary to achieve accurate readings.