Welcome to the World of Resistance!
Hi there! In this chapter, we are going to explore why some materials are great at carrying electricity while others try to slow it down. This concept is called Resistance. It’s a fundamental part of the "Energy, power and resistance" section of your OCR Physics A course. Understanding resistance is like understanding the "friction" of the electrical world—it helps us control energy and build everything from simple flashlights to complex smartphones.
1. What exactly is Resistance?
Imagine you are trying to run through a corridor. If the corridor is empty, you can run fast. If the corridor is packed with people bumping into you, you slow down. In a wire, electrons are the runners, and the metal ions in the wire are the people they bump into. This "slowing down" effect is what we call resistance.
The Definition
Resistance (R) is defined as the ratio of the potential difference (p.d.) across a component to the current flowing through it.
The Formula:
\( R = \frac{V}{I} \)
Where:
\( R \) = Resistance measured in Ohms (\(\Omega\))
\( V \) = Potential Difference measured in Volts (V)
\( I \) = Current measured in Amperes (A)
Quick Review: The Ohm
One Ohm (\(1 \Omega\)) is defined as the resistance of a component when a potential difference of 1V produces a current of 1A.
Memory Aid: Just remember the "V-I-R" triangle! Put V at the top, and I and R at the bottom. To find R, cover it with your finger, and you see V over I.
Key Takeaway: Resistance tells us how many Volts are needed for every Ampere of current. High resistance means you need a lot of "push" (Voltage) to get the current moving.
2. Ohm’s Law
You’ll hear this name a lot! Georg Ohm discovered a specific rule that applies to some materials (mostly metals) at a constant temperature.
Ohm’s Law states: The current through a conductor is directly proportional to the potential difference across it, provided the physical conditions (like temperature) remain constant.
What does this look like on a graph?
If you plot Current (\(I\)) on the y-axis and Potential Difference (\(V\)) on the x-axis, you get a straight line through the origin. The steeper the line, the lower the resistance!
Don't worry if this seems tricky: Not every component follows this law. Components that do are called Ohmic conductors. Those that don't are Non-Ohmic.
3. I-V Characteristics: How Different Components Behave
In your practicals (PAG3), you will measure how current changes as you change the voltage for different things. Here is what you need to know for the exam:
A. Fixed Resistor (Ohmic Conductor)
A straight line through the origin. Resistance stays the same no matter which way the current flows or how much voltage you apply.
B. Filament Lamp (Non-Ohmic)
The graph looks like an "S" shape.
Why? As the current increases, the wire gets hotter. The metal ions vibrate more, making it harder for electrons to get past. Therefore, as temperature increases, resistance increases.
C. Diodes and LEDs (Non-Ohmic)
A diode is like a one-way street for electricity.
- In one direction (reverse bias), the resistance is massive, so no current flows.
- In the other direction (forward bias), nothing happens until you hit a "threshold voltage" (usually 0.6V), then the resistance drops suddenly and current flows easily.
Did you know? LEDs (Light Emitting Diodes) are just diodes that glow! They are much more energy-efficient than filament lamps because they don't rely on getting hot to produce light.
Key Takeaway: If the \(I-V\) graph is a straight line, resistance is constant. If it's a curve, resistance is changing.
4. Environmental Sensors: LDRs and Thermistors
Some components are designed to change their resistance based on the world around them.
The LDR (Light-Dependent Resistor)
The Rule: LURD — Light Up, Resistance Down.
In bright light, an LDR has low resistance. In the dark, it has high resistance. This makes them perfect for automatic streetlights!
The NTC Thermistor
NTC stands for Negative Temperature Coefficient.
The Rule: As Temperature Up, Resistance Down.
This is the opposite of a normal metal wire. These are used in digital thermometers and thermostats.
Quick Review Box:
- Metals: Temp \( \uparrow \), Resistance \( \uparrow \)
- NTC Thermistors: Temp \( \uparrow \), Resistance \( \downarrow \)
- LDRs: Light \( \uparrow \), Resistance \( \downarrow \)
5. Resistivity: The "Nature" of the Material
Resistance depends on the shape of an object (how long or thick a wire is). But Resistivity (\(\rho\)) is a property of the material itself, regardless of its shape.
The Factors Affecting Resistance:
1. Length (\(L\)): Doubling the length doubles the resistance (more "people" to bump into). \( R \propto L \)
2. Cross-sectional Area (\(A\)): Doubling the area halves the resistance (more lanes in the "corridor"). \( R \propto \frac{1}{A} \)
The Resistivity Equation:
\( R = \frac{\rho L}{A} \)
Or, rearranged to find resistivity:
\( \rho = \frac{RA}{L} \)
Units: Resistivity is measured in Ohm-metres (\(\Omega m\)).
Common Mistake: Don't confuse Resistance and Resistivity!
Analogy: Resistance is like how hard it is to squeeze through a specific pipe. Resistivity is like how "sticky" the liquid inside is. A long pipe has more resistance, but the "stickiness" (resistivity) of the liquid stays the same.
Step-by-Step: Determining Resistivity in the Lab
1. Measure the diameter of the wire using a micrometer in several places to find the average.
2. Calculate the area \( A = \pi r^2 \) (remember \( r \) is half the diameter!).
3. Measure the resistance \( R \) for different lengths \( L \).
4. Plot a graph of \( R \) (y-axis) against \( L \) (x-axis).
5. The gradient of your graph will be \( \frac{R}{L} \).
6. Multiply the gradient by the area \( A \) to get the resistivity \( \rho \)!
6. Why does Temperature change Resistance?
This is a favorite exam question! Here is how to answer it for two different materials:
In Metals (Conductors):
Metals are made of a lattice of positive ions. When it gets hotter, these ions vibrate with more kinetic energy. This makes it much more likely that the flowing electrons will collide with the ions. More collisions = more resistance.
In Semiconductors (like Thermistors):
Semiconductors have very few free electrons at room temperature. When you heat them up, the energy "shakes" more electrons free from their atoms. This increase in the number density of charge carriers (\(n\)) is so huge that it outweighs the extra vibrations. More charge carriers = lower resistance!
Key Takeaway: Metals get worse at conducting when hot; semiconductors get better.
Final Quick Check!
Before you move on, can you:
- Define resistance and state its unit? (\( R=V/I \), Ohms)
- Sketch an \(I-V\) graph for a filament lamp and explain its shape? (Temperature effects)
- State the LURD rule for LDRs?
- Use the resistivity formula \( \rho = \frac{RA}{L} \)?
If you can do these, you're in great shape for this chapter! Keep going—Physics gets easier the more you practice these core links.