Internal Resistance A Level Physics

Internal Resistance: A Deep Dive into A-Level Physics

Internal resistance is a crucial concept in A-Level Physics, often causing confusion among students. Understanding it is essential for mastering circuits and electromotive force (emf). This comprehensive guide will break down internal resistance, explaining its nature, effects, and how to calculate it, leaving you with a firm grasp of this vital topic. We'll explore its implications in real-world applications and address common student questions, ensuring you're well-prepared for your exams.

Introduction: What is Internal Resistance?

Every real-world power source, whether it's a battery, cell, or power supply, possesses internal resistance. This isn't a separate resistor connected in series; it's an inherent property of the source itself, stemming from the materials and chemical processes within it. Imagine the internal workings of a battery: the chemical reactions producing the electrical potential energy encounter resistance as the electrons move through the electrolyte and electrode materials. This resistance impedes the flow of current, resulting in a voltage drop within the power source. This voltage drop is directly proportional to the current flowing through the source.

Understanding internal resistance is crucial because it affects the potential difference (voltage) available across the external circuit components. It's not just an abstract concept; it impacts the performance of electrical devices and systems significantly. Ignoring internal resistance leads to inaccurate calculations and a flawed understanding of circuit behavior.

The Electromotive Force (emf) and Terminal Potential Difference (V)

Before diving deeper into calculations, let's clarify two key terms:

• Electromotive Force (emf, ε): This represents the total energy supplied per coulomb of charge by the source. It's the maximum potential difference the source could provide if there were no internal resistance. Think of it as the battery's ideal voltage.

• Terminal Potential Difference (V): This is the actual potential difference across the terminals of the power source when a current is flowing. It's the voltage measured using a voltmeter connected across the battery terminals. It's always less than the emf due to the voltage drop across the internal resistance.

The relationship between emf, terminal potential difference, internal resistance, and external resistance is fundamental to understanding circuit behavior.

Understanding the Circuit with Internal Resistance

Let's consider a simple circuit: a cell with internal resistance (r) connected to an external resistor (R). When the circuit is closed, current (I) flows. The emf (ε) is divided across two components:

1. The external resistor (R): This experiences a potential difference equal to IR (Ohm's Law).

2. The internal resistor (r): This experiences a potential difference equal to Ir (Ohm's Law).

Therefore, the terminal potential difference (V) across the battery terminals is given by:

V = ε - Ir

This equation is a cornerstone of understanding internal resistance. It shows that the terminal potential difference decreases as the current increases – a direct consequence of the voltage drop across the internal resistance.

Determining Internal Resistance: Practical Methods

Several methods allow us to determine the internal resistance of a cell or battery. Here are two common approaches:

1. The Variable Resistor Method

This method involves connecting a variable resistor (rheostat) in series with the cell. By varying the resistance of the rheostat, we can alter the current flowing through the circuit. We measure the current (I) and the corresponding terminal potential difference (V) using an ammeter and voltmeter, respectively, for several different values of R.

Plotting a graph of V against I, we obtain a straight line with a negative gradient. The y-intercept of this graph represents the emf (ε), and the negative gradient equals the internal resistance (r). This graphical method provides a visual representation of the relationship and allows for a more accurate determination of both emf and internal resistance.

2. The Short Circuit Method (Less Precise)

In this method, we briefly connect a very low resistance across the cell's terminals. The current (I_short) is then measured. Since the external resistance is negligible compared to the internal resistance, the terminal potential difference is approximately zero. The equation simplifies to:

ε ≈ I_shortr

Therefore, the internal resistance can be estimated as:

r ≈ ε / I_short

This method is less accurate because it relies on the assumption of a near-zero external resistance, which is difficult to achieve in practice. Also, the high current during the short circuit can damage the cell.

Illustrative Examples and Calculations

Let's work through some example problems to solidify our understanding:

Example 1: A cell has an emf of 1.5 V and an internal resistance of 0.5 Ω. It's connected to an external resistor of 2.0 Ω. Calculate the current flowing in the circuit and the terminal potential difference across the cell.

• Total resistance: R_total = R + r = 2.0 Ω + 0.5 Ω = 2.5 Ω
• Current: I = ε / R_total = 1.5 V / 2.5 Ω = 0.6 A
• Terminal potential difference: V = ε - Ir = 1.5 V - (0.6 A)(0.5 Ω) = 1.2 V

Example 2: A cell is connected to a variable resistor. The following data is obtained:

Plot this data and determine the emf and internal resistance of the cell.

By plotting this data and drawing a best-fit line, we can find the y-intercept (emf) and the gradient (negative of the internal resistance). The y-intercept would represent the emf, and the negative of the slope would provide the internal resistance.

Advanced Concepts and Applications

The concept of internal resistance extends beyond simple circuits. Here are some advanced considerations:

• Temperature dependence: Internal resistance often changes with temperature. Higher temperatures generally lead to increased internal resistance in some types of cells, affecting their performance.

• Ageing effects: As batteries age, their internal resistance increases, leading to reduced performance and shorter operating times.

• Different types of cells: Various cells (e.g., dry cells, lead-acid batteries, fuel cells) exhibit different internal resistance characteristics. These differences are related to the materials used and the electrochemical processes involved.

• Parallel and Series Combinations: Understanding how internal resistance affects the equivalent emf and internal resistance in parallel and series combinations of cells is important for designing complex circuits.

• Maximum Power Transfer Theorem: This theorem states that maximum power is transferred from a source to a load when the load resistance equals the source's internal resistance. This is a crucial consideration in many electronic applications.

Frequently Asked Questions (FAQ)

• Q: Why is internal resistance important? A: Because it reduces the actual voltage available to the external circuit, affecting the performance of connected devices and leading to inaccurate calculations if ignored.

• Q: Can internal resistance be eliminated? A: No, it's an inherent property of the power source. However, engineers strive to minimize it through material selection and design improvements.

• Q: How does internal resistance affect battery life? A: Increased internal resistance reduces the available energy and can shorten battery life.

• Q: What is the difference between emf and terminal potential difference? A: Emf is the maximum potential difference a source can provide without internal resistance, while the terminal potential difference is the actual voltage available across the terminals under load.

• Q: Can internal resistance be negative? A: No, resistance is always a positive value.

Conclusion

Internal resistance is a fundamental concept in A-Level Physics that is crucial for a thorough understanding of circuits and electrical power sources. By grasping the relationship between emf, terminal potential difference, and internal resistance, you can accurately analyze and predict circuit behavior. Mastering the techniques for determining internal resistance is essential for practical applications and exam success. Remember to practice calculations and apply the concepts in diverse circuit scenarios to build a strong foundation in this critical area of physics. Understanding internal resistance isn't just about passing exams; it's about developing a deeper understanding of how real-world electrical systems function.