Resistance, resistivity and internal resistance

Welcome to the World of Circuits!

Hi there! Today we are diving into one of the most practical chapters in Physics: Resistance, Resistivity, and Internal Resistance. Have you ever wondered why your phone gets warm while charging, or why a lightbulb glows? It all comes down to how materials "fight back" against electricity. Don't worry if these terms sound a bit technical—we're going to break them down step-by-step with simple analogies and clear examples. Let's get started!

1. What is Resistance?

At its simplest, resistance is a measure of how much a component opposes the flow of electric current. Think of it like a crowded corridor: if the corridor is empty, you can run through easily (low resistance). If it’s packed with people, you have to push and shove to get through (high resistance).

The Mathematical Definition

In Physics, we define resistance (R) as the ratio of the potential difference (V) across a component to the current (I) flowing through it. We use the formula:

\( R = \frac{V}{I} \)

Where:
- \( R \) is Resistance measured in Ohms (\(\Omega\)).
- \( V \) is Potential Difference measured in Volts (V).
- \( I \) is Current measured in Amperes (A).

Quick Review: The Ohm

One Ohm is defined as the resistance of a component when a potential difference of 1 Volt produces a current of 1 Ampere.

Common Mistake to Avoid: Don't confuse Resistance with Resistivity! Resistance depends on the specific object (its size and shape), while resistivity depends only on the material itself. We’ll look at that next!

2. Resistivity: The "DNA" of a Material

Why does a copper wire conduct electricity better than a glass rod? It’s because of resistivity (\(\rho\)). While resistance depends on the shape of the wire, resistivity is a property of the material itself.

The Resistance Formula

The resistance of a wire depends on three things:
1. Length (\(l\)): Longer wires have more resistance (more "corridor" to push through).
2. Cross-sectional Area (\(A\)): Thicker wires have less resistance (more lanes for the "traffic" to flow).
3. Resistivity (\(\rho\)): How naturally "stubborn" the material is.

The formula is:
\( R = \frac{\rho l}{A} \)

Analogy: Think of water flowing through a pipe. A longer pipe makes it harder for water to get to the end. A wider pipe makes it much easier. The "roughness" of the inside of the pipe is like the resistivity.

Memory Aid: Remember "RE-L-A". Resistance equals rho times Length over Area.

Key Takeaway: To get the lowest resistance, you want a short, thick wire made of a material with low resistivity (like copper).

3. I-V Characteristics: Reading the Graphs

Not every component behaves the same way when you change the voltage. We use I-V Characteristic graphs (Current vs. Voltage) to see how they behave.

A. Ohmic Resistors (Fixed Resistors)

For these components, current is directly proportional to potential difference (provided temperature is constant).
- Graph: A straight line passing through the origin.
- Takeaway: The resistance is constant.

B. Filament Lamps

As the voltage increases, the filament gets hotter.
- Graph: An "S" shaped curve that levels off at higher voltages.
- Why? As temperature increases, the metal atoms vibrate more, making it harder for electrons to pass through. So, resistance increases as current increases.

C. Semiconductor Diodes

Diodes are like one-way streets for electricity.
- Graph: Zero current for negative voltages, then a sharp spike in current after a certain positive voltage (the threshold voltage).
- Takeaway: They have very high resistance in one direction and very low resistance in the other.

D. NTC Thermistors

NTC stands for Negative Temperature Coefficient.
- Behavior: Unlike metals, when a thermistor gets hotter, its resistance decreases.
- Graph: The slope of the I-V graph increases as voltage increases.

4. Why does Temperature affect Resistance?

This is a favorite exam question! To explain this, we look at two microscopic factors: Number Density (\(n\)) and Drift Velocity (\(v\)).

In Metals (e.g., Filament Lamps)

1. When a metal gets hot, its positive ions vibrate more vigorously.
2. These vibrating ions collide more frequently with the flowing electrons.
3. This reduces the drift velocity of the electrons.
4. Therefore, resistance increases.

In Semiconductors (e.g., NTC Thermistors)

1. When a semiconductor gets hot, the thermal energy "shakes loose" more charge carriers (electrons).
2. This significantly increases the number density (\(n\)) of available charge carriers.
3. This effect is much stronger than the increase in collisions.
4. Therefore, resistance decreases.

Did you know? This is why your laptop or phone might slow down if it gets too hot—the heat changes how the internal circuits conduct electricity!

5. Internal Resistance: The Battery's Secret

Have you ever noticed that a battery feels warm after use? That’s because batteries aren't perfect. They have their own internal resistance (\(r\)).

E.M.F vs. Terminal Potential Difference

- E.M.F. (\(\epsilon\)): The total energy the battery supplies to each unit of charge.
- Terminal P.D. (\(V\)): The actual voltage that makes it out of the battery to the rest of the circuit.

Because of internal resistance, some voltage is "lost" inside the battery. We call these "lost volts".

The equation is:
\( \epsilon = V + Ir \)
or
\( V = \epsilon - Ir \)

Example: If a battery has an e.m.f. of 9V but is currently losing 1V internally, the terminal P.D. available to your circuit is only 8V.

The Effect on Output Power

As you draw more current from a battery, the "lost volts" (\(Ir\)) increase, and the terminal P.D. (\(V\)) drops. This is why a car’s headlights might dim slightly when you start the engine—the starter motor draws a huge current, causing a large internal voltage drop!

Quick Review Box:
- E.M.F is the "Total Voltage".
- Terminal P.D. is "What’s left for the circuit".
- Ir is the "Lost Volts" spent overcoming internal resistance.

Summary Checklist

Before you move on to practice problems, make sure you can:
- [ ] Define resistance using \( V = IR \).
- [ ] Calculate resistance using length, area, and resistivity (\( R = \rho l / A \)).
- [ ] Sketch I-V graphs for a resistor, lamp, diode, and thermistor.
- [ ] Explain why a thermistor's resistance drops when heated (Number density increases).
- [ ] Use the e.m.f equation \( \epsilon = V + Ir \) to find internal resistance or terminal P.D.

Don't worry if the math for internal resistance seems tricky at first. Just remember: Total Volts = Used Volts + Lost Volts. You've got this!