Resistance

Intros
Lessons
1. Introduction to resistors and resistance:
2. Another review on circuits so far.
3. What is resistance?
4. How do you add resistors in series?
5. How do you add resistors in parallel?
6. How is resistance affected by series and parallel configurations?
Examples
Lessons
1. Solving Resistance for Resistors in Series
Find the total resistance of the circuit.

1. Solving Resistance for Resistors in Parallel
Find the total resistance of the circuit.

1. Solving for Resistors in BOTH Series & Parallel Configurations

1. Find the total resistance for resistors in parallel configuration.
2. Find the total resistance for the entire circuit.
2. Solving for More Resistors in BOTH Series & Parallel Configurations
Find the total resistance for the entire circuit.

Introduction to Electrical Resistance

Welcome to our lesson on electrical resistance, a fundamental concept in understanding how circuit components interact. As introduced in our video, resistance plays a crucial role in controlling the flow of electric current. This lesson will delve into the basics of resistance, exploring its measurement and significance in electrical circuits. We'll examine how resistance affects the behavior of electrons in conductors and how it relates to other electrical properties. Understanding resistance is key to grasping Ohm's law, which forms the foundation of electrical circuit analysis. Throughout this lesson, we'll explore various materials and their resistive properties, learning how to calculate and manipulate resistance in practical applications. By the end, you'll have a solid grasp of how resistance shapes the functionality of electrical systems, from simple household appliances to complex electronic devices.

Understanding Electrical Resistance

Electrical resistance is a fundamental concept in the world of electronics and electrical engineering. It refers to the opposition that a material or component presents to the flow of electric current. This property plays a crucial role in the design and operation of electrical circuits, influencing how energy is distributed and consumed within a system.

At its core, resistance impedes the flow of electric current through a conductor. Think of it as a bottleneck in a water pipe; just as a narrow section slows down water flow, resistance restricts the movement of electrons. This impediment is essential for controlling current in circuits, allowing for the precise manipulation of electrical energy.

The unit of measurement for electrical resistance is the ohm, symbolized by the Greek letter Ω (omega). This unit is named after the German physicist George Simon Ohm, who made significant contributions to the study of electricity in the early 19th century. One ohm represents the resistance between two points of a conductor when a potential difference of one volt across these points produces a current of one ampere.

To understand the relationship between resistance, voltage, and current, we can use a simple analogy. Imagine a water tank connected to a pipe. The water pressure in the tank is like voltage, the flow rate of water through the pipe is akin to electric current, and the pipe's diameter represents resistance. Just as a narrower pipe (higher resistance) reduces water flow for a given pressure, higher electrical resistance reduces current flow for a given voltage.

This relationship is formalized in Ohm's Law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. Mathematically, this is expressed as V = IR, where V is voltage, I is current, and R is resistance.

Resistance in electrical circuits serves various purposes. It can be used to limit current flow, divide voltage, generate heat, or create light (as in incandescent bulbs). In complex circuits, resistors are used to protect sensitive components from excessive current, adjust signal levels, and create timing circuits.

The concept of resistance extends beyond simple resistors. All materials exhibit some level of resistance, even good conductors like copper wire. This inherent resistance becomes significant in long-distance power transmission, where it can lead to energy losses. Superconductors, materials with virtually zero resistance at extremely low temperatures, represent the opposite extreme and are the subject of ongoing research for their potential in energy-efficient technologies.

Understanding resistance is crucial for anyone working with electrical systems. It allows engineers to design circuits that efficiently manage power, control signals, and protect components. For instance, in LED lighting, resistors are used to limit current and prevent the LEDs from burning out. In audio equipment, variable resistors (potentiometers) allow users to adjust volume by changing the resistance in the circuit.

As technology advances, the management of resistance becomes increasingly sophisticated. In modern microprocessors, for example, engineers must carefully control resistance at the nanoscale to optimize performance and energy efficiency. The ongoing challenge is to balance the need for resistance in certain parts of a circuit with the desire to minimize it in others to reduce power transmission loss and heat generation.

In conclusion, electrical resistance is a fundamental property that shapes the behavior of all electrical systems. From the simplest household appliance to the most complex electronic devices, resistance plays a vital role in controlling current, managing power, and enabling the functionality we rely on in our modern, electrified world. By understanding resistance and its relationship with voltage and current, we gain insight into the invisible forces that power our technological society.

Resistors in Series Circuits

Resistors in series circuits play a crucial role in controlling current flow and voltage distribution in electrical systems. Understanding how these components work together is essential for anyone studying electronics or working with electrical circuits. In this section, we'll explore the concept of resistors in series, their behavior, and how to calculate total resistance.

What is a Series Circuit?

A series circuit is an arrangement where components are connected end-to-end, forming a single path for current to flow. In the case of resistors in series, they are connected one after another, with the same current passing through each resistor.

Current Flow in Series Circuits

In a series circuit, the current flowing through each resistor is identical. This is because there is only one path for the current to follow. If we measure the current at any point in the circuit, we'll find it to be the same.

Voltage Drop Across Resistors

While the current remains constant, the voltage drop across each resistor in a series circuit can vary. The voltage drop depends on the resistance value of each component. The sum of these individual voltage drops equals the total voltage supplied by the source.

Calculating Total Resistance

One of the most important aspects of working with resistors in series is understanding how to calculate the total resistance. The formula for total resistance in a series circuit is straightforward:

Rtotal = R1 + R2 + R3 + ... + Rn

Where Rtotal is the total resistance, and R1, R2, R3, etc., are the individual resistor values.

Example Calculation

Let's consider a series circuit with three resistors: 10Ω, 20Ω, and 30Ω. To find the total resistance:

Rtotal = 10Ω + 20Ω + 30Ω = 60Ω

Practical Applications

Series circuits with resistors are commonly used in various applications, including:

• Voltage dividers
• LED current limiting
• Temperature sensors
• Audio volume controls

Practice Problems

To reinforce your understanding, try solving these problems:

1. Calculate the total resistance of a series circuit containing resistors of 100Ω, 220Ω, and 330Ω.
2. If a 9V battery powers a series circuit with resistances of 1kΩ, 2kΩ, and 3kΩ, what is the current flowing through the circuit?
3. In a series circuit with a total resistance of 500Ω and a supply voltage of 12V, what is the voltage drop across a 150Ω resistor?

Understanding resistors in series circuits is fundamental to electrical engineering and circuit design. By grasping these concepts, you'll be better equipped to analyze and create more complex circuits. Remember that in series circuits, the current remains constant while voltage drops are distributed across the resistors. The total resistance is simply the sum of all individual resistances, making calculations straightforward. Practice with various configurations to solidify your knowledge and improve your problem-solving skills in circuit analysis.

Resistors in Parallel Circuits

Parallel circuits are fundamental in electrical engineering, offering unique characteristics that differ significantly from series circuits. In a parallel configuration, resistors are connected across the same voltage source, creating multiple paths for current flow. This arrangement has profound implications for how resistors function and how we calculate total resistance.

Series vs. Parallel Configurations

In a series circuit, resistors are connected end-to-end, forming a single path for current. Conversely, in a parallel circuit, each resistor forms a separate branch, allowing current to divide among multiple paths. This fundamental difference affects voltage distribution and current flow.

Functioning of Resistors in Parallel

When resistors are connected in parallel, they all experience the same voltage across their terminals. This is a key principle of parallel circuits. However, the current through each resistor can differ based on its resistance value. This phenomenon is known as current division.

Calculating Total Resistance in Parallel

The formula for calculating total resistance in a parallel circuit is:

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

Where Rtotal is the total resistance and R1, R2, R3, etc., are individual resistor values. This reciprocal relationship means that the total resistance in a parallel circuit is always less than the smallest individual resistor.

Current Division in Parallel Circuits

The current in a parallel circuit divides among the branches inversely proportional to their resistances. This means that branches with lower resistance will carry more current than those with higher resistance. The total current entering the parallel section equals the sum of currents in all branches.

Voltage Distribution

Unlike series circuits where voltage drops across resistors, in parallel circuits, the voltage remains constant across all branches. This property makes parallel circuits ideal for applications where a consistent voltage supply is needed for multiple components.

Practical Examples

1. Home Electrical Systems: Most household electrical circuits are wired in parallel. This allows devices to operate independently at the same voltage.

2. LED Arrays: Multiple LEDs are often connected in parallel to maintain consistent brightness while sharing current.

Practice Problem

Calculate the total resistance of a parallel circuit containing three resistors: 10Ω, 20Ω, and 30Ω.

Solution:

1/Rtotal = 1/10 + 1/20 + 1/30
1/Rtotal = 0.1 + 0.05 + 0.0333 = 0.1833
Rtotal = 1 / 0.1833  5.45Ω

1. Consistent Voltage: All components receive the same voltage, regardless of their individual resistances.

2. Independent Operation: Failure of one component doesn't affect others in the circuit.

3. Flexibility: Easy to add or remove components without significantly altering the circuit's overall characteristics.

Conclusion

Understanding how resistors function in parallel circuits is crucial for designing and analyzing electrical systems. The unique properties of parallel configurations, including current division and constant voltage distribution, make them indispensable in various applications. By mastering the concepts and calculations involved, engineers and hobbyists can effectively utilize parallel circuits in their projects, optimizing performance

Comparing Series and Parallel Resistor Configurations

When designing electrical circuits, understanding the differences between series and parallel resistor configurations is crucial. These two circuit configurations offer distinct advantages and disadvantages, affecting the total resistance and current flow in unique ways. Let's explore the characteristics of series vs parallel configurations and their practical applications.

In a series configuration, resistors are connected end-to-end, forming a single path for current flow. The total resistance in a series circuit is the sum of all individual resistor values. This means that adding more resistors in series increases the overall resistance. One advantage of series circuits is their simplicity and ability to divide voltage across components. However, a drawback is that if one resistor fails, the entire circuit is interrupted.

Conversely, parallel configurations connect resistors across common points, creating multiple paths for current flow. The total resistance in a parallel circuit is always less than the smallest individual resistor value. As more resistors are added in parallel, the total resistance decreases. Parallel circuits offer the advantage of maintaining functionality even if one resistor fails, as current can still flow through other paths. They also allow for equal voltage distribution across all components.

The choice between series and parallel configurations depends on the specific requirements of the circuit. Series configurations are often used in applications where voltage division is needed, such as in voltage dividers or in some types of sensors. They're also common in battery-powered devices, where multiple cells are connected in series to increase the total voltage.

Parallel configurations find extensive use in household electrical systems, where multiple appliances need to operate at the same voltage. They're also crucial in power distribution networks, allowing for the connection of multiple loads without significantly affecting the overall circuit resistance. In electronic devices, parallel resistors are often used to create precise resistance values or to handle higher power dissipation.

Understanding these circuit configurations is essential for engineers and hobbyists alike. Series circuits offer simplicity and voltage division but are vulnerable to single-point failures. Parallel circuits provide redundancy and maintain consistent voltage across components but require more complex calculations for total resistance. By carefully considering the advantages and limitations of each configuration, designers can create efficient and reliable electrical systems tailored to specific needs.

Ohm's Law and Resistance

Ohm's Law is a fundamental principle in electrical engineering that describes the relationship between voltage, current, and resistance in an electrical circuit. This law, formulated by German physicist Georg Ohm, is expressed by the equation V = IR, where V represents voltage (measured in volts), I represents current (measured in amperes), and R represents resistance (measured in ohms).

Understanding Ohm's Law is crucial for calculating resistance and solving various electrical problems. The law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. This means that as voltage increases, current increases, and as resistance increases, current decreases.

To use Ohm's Law for resistance calculation, you can rearrange the equation to solve for R: R = V / I. This allows you to determine the resistance when you know the voltage and current. Similarly, you can calculate voltage (V = IR) or current (I = V / R) when the other two variables are known.

Let's look at some examples to reinforce understanding:

1. If a circuit has a voltage of 12V and a current of 2A, the resistance can be calculated as R = V / I = 12V / 2A = 6Ω.
2. In a circuit with a resistance of 100Ω and a current of 0.5A, the voltage would be V = IR = 0.5A * 100Ω = 50V.
3. For a 9V battery connected to a 3Ω resistor, the current flow would be I = V / R = 9V / 3Ω = 3A.

Practice problems:

1. Calculate the resistance in a circuit with 24V and 3A of current.
2. Determine the voltage needed to push 0.1A through a 220Ω resistor.
3. Find the current in a circuit with 5V and a resistance of 2.5Ω.

Ohm's Law is not just a theoretical concept; it has practical applications in designing and troubleshooting electrical systems. Engineers and technicians use it to determine appropriate component values, analyze circuit behavior, and ensure safe operation of electrical devices. By mastering Ohm's Law and resistance calculations, you'll have a powerful tool for understanding and working with electrical circuits in various fields, from electronics to power systems.

Conclusion

In this lesson, we've explored the fundamental concept of electrical resistance and its crucial role in circuit analysis. We've learned how resistance opposes the flow of electric current, and how it's measured in ohms. We've also delved into Ohm's law, which relates voltage, current, and resistance. Understanding resistance is essential for anyone working with electrical circuits, from simple household wiring to complex electronic devices. To reinforce your knowledge, we encourage you to revisit the introductory video and dedicate time to solving practice problems. These exercises will help solidify your grasp of resistance calculations and their applications. As you continue your journey in electrical engineering, remember that mastering resistance is a stepping stone to more advanced concepts. We invite you to explore further resources on our website and join our online community to discuss and share insights about electrical resistance and related topics. Keep experimenting and learning!

Introduction to Resistors and Resistance: Another Review on Circuits So Far

In this guide, we will delve into the fundamental concepts of resistors and resistance, providing a comprehensive review of electric circuits. This will help solidify your understanding of how these components function within a circuit.

Step 1: Understanding Electric Circuits

To begin, let's refresh our knowledge of what an electric circuit is. An electric circuit is a closed loop that allows current to flow through it. The main components of a circuit include a power source (such as a battery), electrical wires, and various other elements like resistors.

The battery provides the voltage, measured in volts (V). This voltage is essential as it drives the current through the circuit. The unit 'volt' is named after Alessandro Volta, an Italian physicist who made significant contributions to the study of electricity.

Step 2: Components of a Circuit

Next, let's discuss the three main components of a circuit:

• Battery: The battery is depicted schematically with a long positive terminal and a shorter negative terminal. It provides the necessary voltage to drive the current through the circuit.
• Electrical Wires: These wires connect the entire circuit, forming a closed loop with no breaks. The current flows through these wires, completing the circuit.
• Resistors: Resistors are components that resist the flow of current, thereby controlling the amount of current that passes through the circuit. They can be connected in series or parallel configurations.

Step 3: Current Flow in Circuits

When discussing current flow, it's important to distinguish between conventional current and electron flow. Conventional current flows from the positive terminal to the negative terminal of the battery. However, in reality, the subatomic particles that carry the charge are electrons, which flow from the negative terminal to the positive terminal. This is known as electron flow or electron current.

In most questions, unless specified otherwise, we assume conventional current flow, which is from the positive to the negative terminal.

Step 4: Focus on Resistors

Resistors are crucial components in a circuit as they control the flow of current. They can be connected in two main ways:

• Series Connection: In a series connection, resistors are connected end-to-end, providing only one path for the current to flow. This means the current is the same through all resistors, but the voltage drop is divided among them.
• Parallel Connection: In a parallel connection, resistors are connected across the same two points, providing multiple paths for the current to flow. This means the voltage across each resistor is the same, but the current is divided among the different paths.

Step 5: Units of Measurement

Understanding the units of measurement for the main concepts in circuits is essential:

• Voltage: Measured in volts (V), named after Alessandro Volta.
• Current: Measured in amperes (A), named after Jean-Marie Ampère, a French physicist.
• Resistance: Measured in ohms (Ω), named after George Simon Ohm, who studied the relationship between voltage, current, and resistance.

Step 6: Historical Context

The units of measurement for voltage, current, and resistance are named after scientists who made significant contributions to the field of electricity:

• Alessandro Volta: An Italian physicist known for his work on the electric battery and the discovery of methane.
• Jean-Marie Ampère: A French physicist and mathematician who is considered one of the founders of the science of classical electromagnetism.
• George Simon Ohm: A German physicist and mathematician who formulated Ohm's Law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points.

Conclusion

By understanding the basic components of a circuit, the flow of current, and the role of resistors, you can gain a deeper insight into how electric circuits function. This knowledge is foundational for further studies in electronics and electrical engineering.

FAQs

1. What is electrical resistance?

Electrical resistance is the opposition that a material or component presents to the flow of electric current. It's measured in ohms (Ω) and is fundamental to understanding how electrical circuits work. Resistance affects the amount of current that flows through a circuit for a given voltage.

2. How do resistors in series and parallel circuits differ?

In series circuits, resistors are connected end-to-end, and the total resistance is the sum of individual resistances. Current is the same through each resistor, but voltage drops across them. In parallel circuits, resistors are connected across the same voltage points. The total resistance is less than the smallest individual resistance, and current divides among the branches while voltage remains constant across all resistors.

3. What is Ohm's Law and how is it used to calculate resistance?

Ohm's Law states that voltage (V) equals current (I) multiplied by resistance (R): V = IR. To calculate resistance, you can rearrange this equation to R = V / I. This means if you know the voltage across a component and the current flowing through it, you can determine its resistance.

4. Why is understanding resistance important in electrical engineering?

Understanding resistance is crucial for designing and analyzing electrical circuits. It helps in controlling current flow, dividing voltage, protecting sensitive components, and managing power dissipation. Knowledge of resistance is essential for everything from simple household wiring to complex electronic devices and power systems.

5. How does temperature affect electrical resistance?

Temperature generally affects electrical resistance. For most metals, resistance increases with temperature due to increased atomic vibrations that impede electron flow. However, some materials like semiconductors may exhibit decreased resistance with increased temperature. This relationship is important in various applications, including temperature sensors and superconductors.

Prerequisite Topics

Understanding the concept of resistance in electrical circuits is fundamental to many areas of physics and engineering. While there are no specific prerequisite topics listed for this subject, it's important to recognize that a solid foundation in basic physics and mathematics can greatly enhance your comprehension of resistance. These foundational skills provide the necessary context and tools to fully grasp the principles of electrical resistance.

Resistance is a key concept in electrical engineering and physics, describing how a material opposes the flow of electric current. To fully appreciate its significance, students should have a basic understanding of electricity and electric circuits. This knowledge forms the backdrop against which resistance can be explored in greater depth.

Although not explicitly listed as prerequisites, familiarity with concepts such as voltage, current, and Ohm's law can significantly aid in understanding resistance. These topics are closely interrelated, and grasping their connections can provide valuable insights into how resistance functions within electrical systems.

Additionally, a basic understanding of mathematical concepts, particularly algebra and simple equations, is beneficial when studying resistance. These mathematical skills allow students to work with formulas related to resistance, such as calculating the resistance of a conductor based on its physical properties.

While not strictly necessary, knowledge of materials science can also enhance one's understanding of resistance. Different materials exhibit varying levels of resistance, and understanding the atomic and molecular structure of materials can shed light on why certain substances are better conductors or insulators than others.

It's worth noting that the study of resistance often leads to more advanced topics in electrical engineering and physics. As such, a solid grasp of resistance can serve as a stepping stone to understanding more complex concepts like capacitance, inductance, and alternating current circuits.

In conclusion, while there are no specific prerequisites listed for the study of resistance, a strong foundation in basic physics, mathematics, and electrical concepts can greatly enhance your understanding of this important topic. As you delve into the subject of resistance, you'll find that it connects to many other areas of electrical engineering and physics, making it a crucial concept to master for further studies in these fields.

In this lesson, we will learn:

• A review on what is an electric circuit and the main components: battery (voltage), closed wire path (current), and devices/resistors that use up electricity (resistance).
• What is resistance?
• What is the difference between connecting your circuit in series vs. parallel configurations for resistors?
• What is a battery and how does it provide voltage for an electric circuit?
• How to solve resistance problems for both series and parallel circuits by using the summation equations for equivalent resistance in series and equivalent resistance in parallel
• $R_{eq(series)} = R_{1} + R_{2} + R_{3} + . . . + R_{n} = \sum_{k=1}^{n} R_{k}$

• $\frac{1} {R_{eq(parallel)}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... + \frac{1}{R_{n}} = R_{n} = \sum_{k=1}^{n} R_{k}$
• OR: $R_{eq(parallel)} = \frac{1} { \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... \frac{1}{R_{n}} } = \frac{1} { \sum_{k=1}^{n} \frac{1}{R_{k}} }$

Notes:

• Resistance is a property of the electronic device (resistor; or even battery and wires can have some resistance too and use up some voltage)
• It is a measure of how difficult it is for charges to travel through the circuit
• Resistors in a circuit represent electronic devices that use up voltage
• The greater the resistance, the bigger the voltage drop
• Resistances of metals are CONSTANT and INDEPENDENT of voltage
• The unit for resistance is the ohm ($\Omega$) and can be determined for a circuit by dividing the voltage by the current (in preview of Ohm’s law: $V=IR$).
• When solving for resistance in series, we must use the summation equation:
• $R_{eq(series)} = R_{1} + R_{2} + R_{3} + . . . + R_{n} = \sum_{k=1}^{n} R_{k}$
• Where all resistors in series are added up for the total resistance
• Thus, Req(series) is greater than any single RK independently; adding more resistors in series will increase the total resistance

• When solving for resistance in parallel, we must use the summation equation:
• $\frac{1} {R_{eq(parallel)}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... + \frac{1}{R_{n}} = R_{n} = \sum_{k=1}^{n} R_{k}$
• OR: $R_{eq(parallel)} = \frac{1} { \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + ... \frac{1}{R_{n}} } = \frac{1} { \sum_{k=1}^{n} \frac{1}{R_{k}} }$
• Where the total resistance is equal to the inverse of the sum of all inverses of resistors (branches) in parallel
• Thus, Req(parallel) is less than any single RK independently; adding more resistors in parallel will decrease the total resistance

• In terms of resistance, the advantage of a series configuration is that the battery will last longer; the greater the resistance, the more difficult it is for the charges to travel; thus, less charge is drawn out of the battery over time (less current)
• A parallel configuration generates lesser resistance, allowing charges to flow freely; thus, more charge is drawn out of the battery over time (more current)