Welcome to AS Level Electricity!
Electricity powers our modern world, from your smartphone to high-speed electric trains. In this chapter of AS 1: Forces, Energy and Electricity, we will explore what is happening at the microscopic level inside electrical circuits. We will look at what charge actually is, how it moves to create current, and how energy is given to and taken from these charges.
Don't worry if physics equations sometimes feel intimidating! We will break every single concept down into small, easy-to-understand steps with everyday analogies, clear definitions, and memory tips.
---1. Electric Charge and Charge Carriers
What is Electric Charge?
Electric charge is a fundamental property of matter. Charge comes in two types: positive (\(+\)) and negative (\(-\)). Objects with like charges repel each other, while opposite charges attract.
• Symbol for charge: \(Q\) (or \(q\))
• Standard International (SI) unit: coulomb (\(\text{C}\))
Quantisation of Charge and the Elementary Charge
Charge is quantised. This means charge only exists in discrete, specific packets. The smallest indivisible packet of free charge is the elementary charge, represented by the symbol \(e\).
\(e = 1.60 \times 10^{-19}\text{ C}\)
• A proton has a charge of \(+e = +1.60 \times 10^{-19}\text{ C}\)
• An electron has a charge of \(-e = -1.60 \times 10^{-19}\text{ C}\)
Any measurable charge \(Q\) on an object is always an integer multiple of \(e\):
\(Q = \pm n e\)
where \(n\) is the number of electrons gained, lost, or transferred (\(n = 1, 2, 3, \dots\)).
What are Charge Carriers?
A charge carrier is any mobile charged particle that moves through a material to produce an electric current:
• In metals (conductors): The charge carriers are free conduction electrons. The positive metal ions are fixed in a crystalline lattice and do not move.
• In electrolytes (liquids/solutions): The charge carriers are mobile positive ions (cations) and negative ions (anions), such as \(\text{Na}^+\) and \(\text{Cl}^-\) ions dissolved in water.
• In gases: When ionised by high voltage or radiation, the charge carriers are electrons and positive ions.
Key Takeaways for Charge:
1. Charge is measured in coulombs (\(\text{C}\)).
2. Elementary charge is \(e = 1.60 \times 10^{-19}\text{ C}\).
3. Charge is quantised: \(Q = n e\).
4. In metal wires, current is purely the flow of delocalised electrons.
2. Electric Current
Defining Electric Current
Electric current is defined as the rate of flow of electric charge past a given point or cross-section in a circuit.
We write this mathematically as:
\(I = \frac{\Delta Q}{\Delta t}\)
where:
• \(I\) is the electric current in amperes (\(\text{A}\))
• \(\Delta Q\) is the quantity of charge that flows in coulombs (\(\text{C}\))
• \(\Delta t\) is the time interval in seconds (\(\text{s}\))
If the current is steady, we often simply write: \(Q = I t\).
Understanding the Ampere (\(\text{A}\))
From the formula \(I = \frac{Q}{t}\), we can see that:
\(1\text{ A} = 1\text{ C s}^{-1}\)
Definition: One ampere is the electric current produced when a charge of one coulomb passes a point in a circuit in one second.
Definition: One coulomb is the amount of charge that passes a point in a circuit when a steady current of one ampere flows for one second (\(1\text{ C} = 1\text{ A s}\)).
Conventional Current vs. Electron Flow
This is one of the most common points of confusion in physics! Let's clear it up:
• Conventional Current: Defined historically before electrons were discovered. It is the flow of charge from the positive terminal (\(+\)) to the negative terminal (\(-\)).
• Electron Flow: Electrons are negatively charged, so they are repelled by the negative terminal and attracted towards the positive terminal. Therefore, electrons flow from negative (\(-\)) to positive (\(+\)).
Rule of thumb: In circuit diagrams, unless explicitly asked about electron movement, current arrows always show conventional current (\(+ \rightarrow -\)).
Key Takeaways for Current:
1. \(I = \frac{\Delta Q}{\Delta t}\)
2. \(1\text{ Ampere} = 1\text{ Coulomb per second}\).
3. Conventional current flows from \(+\) to \(-\); electrons flow from \(-\) to \(+\).
3. Microscopic View of Current: Drift Velocity
What Really Happens Inside a Wire?
When no battery is connected, free electrons inside a metal move randomly at very high thermal speeds (around \(10^5\text{ m s}^{-1}\) to \(10^6\text{ m s}^{-1}\)), constantly colliding with the vibrating metal ions. Because their motion is completely random, there is no net movement of charge in any direction, so the current is zero.
When an electric field is applied (by connecting a cell or power supply), a steady electrostatic force acts on the free electrons. They continue to bounce around randomly, but they now slowly drift towards the positive terminal. This slow average net speed is called the mean drift velocity (\(v\)).
The Transport Equation: \(I = nAve\)
The electric current through a conductor is related to its microscopic properties by the formula:
\(I = n A v e\)
Let's define each term carefully:
• \(I\) = Electric current in amperes (\(\text{A}\))
• \(n\) = Number density of free charge carriers (the number of free conduction electrons per unit volume), measured in \(\text{m}^{-3}\)
• \(A\) = Cross-sectional area of the conductor in square metres (\(\text{m}^2\))
• \(v\) = Mean drift velocity of the charge carriers in metres per second (\(\text{m s}^{-1}\))
• \(e\) = Elementary charge (\(1.60 \times 10^{-19}\text{ C}\))
Step-by-Step Derivation of \(I = nAve\):
Step 1: Consider a cylindrical wire of cross-sectional area \(A\). In a time \(\Delta t\), an electron drifting with speed \(v\) travels a distance \(\Delta x = v \Delta t\).
Step 2: The volume of the wire that the electrons pass through in this time is \(\text{Volume} = A \times \Delta x = A v \Delta t\).
Step 3: If there are \(n\) free electrons per unit volume, the total number of electrons in this volume is \(N = n \times \text{Volume} = n A v \Delta t\).
Step 4: The total charge \(\Delta Q\) carried by these electrons is \(\Delta Q = N e = n A v e \Delta t\).
Step 5: Using the definition of current \(I = \frac{\Delta Q}{\Delta t}\):
\(I = \frac{n A v e \Delta t}{\Delta t} \implies I = n A v e\)
Did You Know? The "Slow Electrons, Fast Light" Paradox
Drift velocity in a typical copper wire is astonishingly slow — often less than \(1\text{ mm s}^{-1}\) (about the speed of a crawling snail!).
Why then does a light bulb turn on instantly when you flick the switch?
Think of a bicycle chain or a pipe already full of water. As soon as you push the pedals, the link at the far wheel moves instantly because all links push together. Similarly, all free electrons throughout the entire wire begin drifting almost simultaneously when the switch closes, because the electric field propagates at nearly the speed of light.
Comparing Conductors, Semiconductors, and Insulators
From \(I = nAve\), we can understand why different materials conduct differently based on their value of \(n\):
• Conductors (e.g., Copper, Aluminium): Very high charge carrier density (\(n \approx 10^{28}\text{ to } 10^{29}\text{ m}^{-3}\)). They conduct large currents easily.
• Semiconductors (e.g., Silicon, Germanium): Moderate charge carrier density (\(n \approx 10^{15}\text{ to } 10^{19}\text{ m}^{-3}\)). When heated, more electrons break free, so \(n\) increases, decreasing resistance.
• Insulators (e.g., Rubber, Glass): Extremely low charge carrier density (\(n \approx 0\)). Almost no free electrons are available to conduct charge.
Key Takeaways for Drift Velocity:
1. Drift velocity \(v\) is the slow, net average movement of charge carriers along a conductor.
2. Formula: \(I = nAve\).
3. If a wire narrows (area \(A\) decreases) while carrying the same current \(I\), the drift velocity \(v\) must increase to maintain the flow.
4. Potential Difference and Electromotive Force
To make charges move around a circuit, energy must be supplied to them and then transferred by them to circuit components (such as bulbs or resistors).
Electromotive Force (e.m.f.)
Electromotive force (e.m.f.), denoted by \(E\) or \(\mathcal{E}\), is associated with a source of electrical energy (such as a battery, solar cell, or generator).
Definition: e.m.f. is the energy converted from other forms (e.g., chemical, mechanical) into electrical energy per unit charge passing through the source.
\(E = \frac{W}{Q}\)
where:
• \(E\) = Electromotive force in volts (\(\text{V}\))
• \(W\) = Energy transferred to electrical energy in joules (\(\text{J}\))
• \(Q\) = Charge in coulombs (\(\text{C}\))
Potential Difference (p.d.)
Potential difference (p.d.), denoted by \(V\), is associated with components that use or dissipate electrical energy (such as lamps, heaters, or resistors).
Definition: Potential difference across a component is the energy converted from electrical energy into other forms (e.g., thermal, light) per unit charge passing through the component.
\(V = \frac{W}{Q}\)
where:
• \(V\) = Potential difference in volts (\(\text{V}\))
• \(W\) = Energy transferred from electrical energy in joules (\(\text{J}\))
• \(Q\) = Charge in coulombs (\(\text{C}\))
Understanding the Volt (\(\text{V}\))
From \(V = \frac{W}{Q}\), the unit of both e.m.f. and p.d. is the volt (\(\text{V}\)):
\(1\text{ V} = 1\text{ J C}^{-1}\)
Definition: One volt is the potential difference between two points when one joule of energy is transferred per one coulomb of charge passing between those points.
Analogy: The Coal Delivery Trucks
Imagine the circuit as a track with delivery trucks (charges):
• The battery (e.m.f.) is the loading depot where trucks are filled with coal (other forms of energy \(\rightarrow\) electrical energy).
• The lamp (p.d.) is the factory where the trucks unload the coal to produce light and heat (electrical energy \(\rightarrow\) other forms of energy).
• The current (\(I\)) is how many trucks pass a checkpoint each second.
Summary Comparison: e.m.f. vs. p.d.
• e.m.f. (\(E\)): Energy transferred TO electrical form per unit charge (at a source / battery).
• p.d. (\(V\)): Energy transferred FROM electrical form per unit charge (at a load / component).
5. Electrical Energy and Electrical Power
Electrical Energy Transferred (\(W\))
Since \(V = \frac{W}{Q}\), the work done or energy transferred by a charge \(Q\) moving across a potential difference \(V\) is:
\(W = Q V\)
Since electric charge is related to current by \(Q = I t\), we can substitute this in to get:
\(W = V I t\)
where:
• \(W\) = Energy transferred in joules (\(\text{J}\))
• \(V\) = Potential difference in volts (\(\text{V}\))
• \(I\) = Current in amperes (\(\text{A}\))
• \(t\) = Time in seconds (\(\text{s}\))
Electrical Power (\(P\))
Power is the rate at which energy is transferred or work is done:
\(P = \frac{W}{t}\)
Substituting \(W = V I t\) into the power equation gives the core electrical power equation:
\(P = V I\)
Using Ohm's law (\(V = I R\)), we can express power in two other very useful forms:
1. Substitute \(V = I R\):
\(P = (I R) \times I \implies P = I^2 R\)
2. Substitute \(I = \frac{V}{R}\):
\(P = V \times \left(\frac{V}{R}\right) \implies P = \frac{V^2}{R}\)
• SI unit of Power: watt (\(\text{W}\)), where \(1\text{ W} = 1\text{ J s}^{-1}\).
When to Use Which Power Formula?
• Use \(P = I^2 R\) when components are connected in series (because current \(I\) is constant throughout a single loop).
• Use \(P = \frac{V^2}{R}\) when components are connected in parallel (because potential difference \(V\) is the same across each parallel branch).
Key Takeaways for Energy and Power:
1. Energy: \(W = Q V = V I t\)
2. Power: \(P = V I = I^2 R = \frac{V^2}{R}\)
3. \(1\text{ Watt} = 1\text{ Joule per second}\).
6. Common Pitfalls & Exam Hints
Common Mistake 1: "Current gets used up as it goes around a circuit."
Incorrect! Charge is conserved. The number of electrons entering a component per second equals the number leaving it per second. Current is the same before and after a resistor. It is energy that is transferred, not current.
Common Mistake 2: Mixing up e.m.f. and p.d. definitions
Always state the direction of energy transformation explicitly in exam definitions:
• e.m.f. = Other forms of energy \(\rightarrow\) Electrical energy per unit charge.
• p.d. = Electrical energy \(\rightarrow\) Other forms of energy per unit charge.
Common Mistake 3: Unit conversion traps
Watch out for metric prefixes in calculations:
• Current in \(\text{mA}\): multiply by \(10^{-3}\) to convert to \(\text{A}\).
• Current in \(\mu\text{A}\): multiply by \(10^{-6}\) to convert to \(\text{A}\).
• Area in \(\text{mm}^2\): multiply by \(10^{-6}\) to convert to \(\text{m}^2\) (since \(1\text{ mm} = 10^{-3}\text{ m}\), so \((10^{-3}\text{ m})^2 = 10^{-6}\text{ m}^2\)).
• Time in minutes: multiply by \(60\) to convert to seconds.
Quick Revision Summary Checklist
Before moving on to the next chapter, check that you can:
• State that charge is quantised and recall \(e = 1.60 \times 10^{-19}\text{ C}\)
• Define electric current as \(I = \frac{\Delta Q}{\Delta t}\) and define the ampere
• State the charge carriers in metals (electrons) and electrolytes (ions)
• Recall, apply, and derive the drift velocity transport equation \(I = n A v e\)
• Define electromotive force (e.m.f.) and potential difference (p.d.) in terms of energy transferred per unit charge (\(W/Q\))
• State the definition of the volt (\(1\text{ V} = 1\text{ J C}^{-1}\))
• Calculate energy transferred using \(W = V I t\) and power using \(P = V I\), \(P = I^2 R\), and \(P = \frac{V^2}{R}\)