Welcome to Sensing!
In this chapter, we are exploring the world of Sensing. This is a vital part of the "Physics in Action" section because, let's face it, our modern world wouldn't work without sensors! From the screen on your smartphone that reacts to your touch, to the sensors in a car that tell the engine how much fuel to use, physics is what makes it happen. We will look at how electricity flows, how we control it, and how we use components like thermistors and LDRs to "feel" the world around us. Don't worry if electricity felt confusing at GCSE; we're going to break it down step-by-step!
1. The Basics: Charge and Current
Before we can sense anything, we need to understand what is moving inside our circuits.
Current as a Flow of Charge
Electric current (I) is simply the rate of flow of charge (Q). Think of it like water flowing through a pipe. The "water" is the charge (measured in Coulombs, C), and the "flow rate" is the current (measured in Amperes, A).
The formula to remember is:
\(I = \frac{\Delta Q}{\Delta t}\)
Example: If 10 Coulombs of charge pass a point in 2 seconds, the current is 5 Amperes.
Charge Carriers
In a metal wire, the charge is carried by tiny electrons. In other materials, like semi-conductors or even salty water, different particles might carry the charge. We call these mobile charge carriers.
Quick Review: Current is just charge on the move. No movement = no current!
2. Potential Difference and Energy
Why does the charge move in the first place? It needs a "push."
Potential Difference (PD)
Potential Difference (V), measured in Volts (V), is defined as the energy transferred per unit charge. When charge moves through a component (like a bulb), it drops off some energy. The PD tells us how much energy each Coulomb of charge "gave away."
The formula is:
\(V = \frac{W}{Q}\)
(Where \(W\) is work done or energy, and \(Q\) is charge).
EMF (Electromotive Force)
While PD is about energy being *spent*, EMF (\(\mathcal{E}\)) is about energy being *given* to the charges by a source, like a battery. It is also measured in Volts. Think of EMF as the "total push" available from the battery.
3. Resistance and Conductance
Not every material lets electricity flow easily. Some materials "resist" the flow, while others "conduct" it well.
Resistance (R)
Resistance is how much a component opposes the flow of current. It's measured in Ohms (\(\Omega\)).
Formula: \(R = \frac{V}{I}\)
Conductance (G)
Conductance is the opposite of resistance. It tells us how easily current flows. It is measured in Siemens (S).
Formula: \(G = \frac{I}{V}\) or \(G = \frac{1}{R}\)
Ohm’s Law
For an Ohmic conductor (like a standard resistor at a constant temperature), the current is directly proportional to the potential difference. If you double the voltage, you double the current. This gives a straight-line graph through the origin on an I-V plot.
Did you know? Not everything follows Ohm's Law! Filaments in lightbulbs change their resistance as they get hot. We call these non-ohmic components.
4. Materials and Resistivity
Why is a copper wire a better conductor than a piece of plastic? It comes down to the number density of mobile charge carriers (n).
- Metals: Have a huge number of free electrons (\(n\) is very high). They conduct very well.
- Semiconductors: Have a medium number of carriers. Their ability to conduct can change with temperature (useful for sensors!).
- Insulators: Have almost no free carriers (\(n\) is very low). They don't conduct.
The Resistivity Formula
The resistance of a wire depends on its length (\(L\)), its cross-sectional area (\(A\)), and the material it's made of (resistivity, \(\rho\)).
\(R = \frac{\rho L}{A}\)
Similarly, for conductance and conductivity (\(\sigma\)):
\(G = \frac{\sigma A}{L}\)
Memory Trick: Think of a hallway. A longer hallway (\(L\)) is harder to get through (more resistance). A wider hallway (\(A\)) is easier to get through (less resistance).
5. Circuits: Series and Parallel
How do we combine these components?
Resistors in Series
Current only has one path. Total resistance is the sum of individual resistances:
\(R_{total} = R_1 + R_2 + ...\)
Resistors in Parallel
Current splits into different branches. Total conductance is the sum:
\(G_{total} = G_1 + G_2 + ...\)
(Or use the fraction formula: \(\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...\))
Common Mistake: In parallel, adding more resistors actually decreases the total resistance because you are providing more paths for the current to flow!
6. Power in Circuits
When current flows, energy is transferred (often as heat). This is called power dissipation.
Power (P) is measured in Watts (W) and can be calculated using:
\(P = IV\)
\(P = I^2 R\)
\(P = \frac{V^2}{R}\)
Quick Review: Power is the rate at which energy is used. A 60W bulb uses 60 Joules of energy every second.
7. Real Batteries: Internal Resistance
In your GCSE problems, batteries were "perfect." In A-Level, we recognize that batteries have their own internal resistance (r). This is why a battery might feel warm when you use it.
The total voltage available (\(\mathcal{E}\)) is split between the "internal" part and the "external" circuit (the load).
The Equation:
\(V = \mathcal{E} - Ir\)
Where \(V\) is the terminal potential difference (what the circuit actually gets) and \(Ir\) is the "lost volts" inside the battery.
8. The Potential Divider (The Heart of Sensors)
A potential divider is a simple circuit that "divides" the input voltage between two resistors. This is the secret to most sensing circuits!
The Formula
If you have two resistors, \(R_1\) and \(R_2\), in series, the output voltage (\(V_{out}\)) across \(R_2\) is:
\(V_{out} = \frac{R_2}{R_1 + R_2} \times V_{in}\)
Using Sensors
If we replace one of those resistors with a sensor, the \(V_{out}\) will change when the environment changes!
- LDR (Light Dependent Resistor): Resistance decreases as light intensity increases (LURD: Light Up, Resistance Down).
- NTC Thermistor: Resistance decreases as temperature increases.
Example: In a night-light, we use an LDR. When it gets dark, the LDR's resistance goes UP, which increases the \(V_{out}\) across it, eventually triggering the light to turn on.
9. Kirchhoff’s Laws
These are just fancy ways of saying that energy and charge are conserved.
Kirchhoff's First Law (Conservation of Charge): The total current entering a junction must equal the total current leaving it. What goes in must come out!
Kirchhoff's Second Law (Conservation of Energy): In any closed loop of a circuit, the sum of the EMFs is equal to the sum of the potential differences.
Chapter Summary Checklist
- Can you define current, PD, and EMF?
- Do you know the difference between resistance and conductance?
- Can you calculate the resistance of a wire using its dimensions and resistivity?
- Do you understand how a potential divider can be used with a thermistor or LDR to create a sensor?
- Can you explain why terminal PD is less than EMF due to internal resistance?
Don't worry if this seems tricky at first! Circuit physics is all about practice. Try drawing the circuits and labeling where the energy is being "pushed" (EMF) and where it is being "spent" (PD), and the math will start to make sense.