Physics | Current and circuits

👋 Welcome to Current and Circuits! (B.5)

Hey there! This chapter might seem like a lot of wires and confusing diagrams, but don't worry. We’re going to look at how electricity moves, focusing on the fundamental particles responsible for that movement—the electrons!

This section, Current and Circuits, sits under the umbrella of The particulate nature of matter. This means we are always going to explain the macroscopic effects (like turning on a light) by understanding the behavior of tiny charged particles (like electrons) inside the wire.

Let’s start flowing!

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Section 1: The Basics of Charge and Current

1.1 Electric Charge (Q)

At its core, electricity is all about Electric Charge. Charge is a fundamental property of matter, much like mass. There are two types: positive (protons) and negative (electrons).

• Key Unit: The unit of charge is the Coulomb (\(C\)).
• Fundamental Charge: The smallest measurable unit of charge belongs to a single electron or proton, denoted as \(e\).
  \(e = 1.60 \times 10^{-19} \, C\)
• Principle: Charge is always quantized, meaning any measurable charge \(Q\) is an integer multiple (\(n\)) of the fundamental charge (\(e\)).
  $$Q = ne$$

1.2 Defining Electric Current (I)

When charged particles (usually electrons in metals) move together in an organized way, we call this an Electric Current.

Current is simply the rate at which charge flows past a specific point in a circuit.

• Definition: Current (\(I\)) is the amount of charge (\(Q\)) passing a point per unit time (\(t\)).
  $$I = \frac{\Delta Q}{\Delta t}$$
• Key Unit: The unit of current is the Ampere (\(A\)). One Ampere is equivalent to one Coulomb per second ($1 \, C s^{-1}$).

💡 Drift Velocity (Linking to Particulate Nature)

In a metal wire, electrons are moving randomly all the time, even when the wire isn't connected to a battery. When you connect a battery, an electric field is established, causing the electrons to acquire a slow net movement in one direction. This average net speed is called the Drift Velocity (\(v\)).

Did you know? While the electrical signal travels near the speed of light, the actual drift velocity of an electron in a typical wire is incredibly slow—often less than 1 millimeter per second! It's like a traffic jam where cars barely move, but the sudden application of brakes (the signal) travels instantly through the entire line of cars.

⚠️ Common Mistake: Conventional Current

Historically, scientists assumed positive charges were doing the moving. Because of this:

• The direction of Conventional Current is defined as the direction positive charge would flow (from the positive terminal to the negative terminal).
• In metal wires, the actual charge carriers are negative electrons, which flow in the opposite direction (from negative terminal to positive terminal).

In IB Physics, unless specifically told otherwise, you must always use the direction of Conventional Current (Positive to Negative) in your diagrams and rules.

Section 2: The Driving Force – Potential Difference and EMF

2.1 Potential Difference (V)

If current is the flow of charge, what causes the flow? You need a "push," which we call Potential Difference (P.D.), or Voltage (\(V\)).

Imagine climbing a hill. You need energy (work) to get to the top. When you roll a ball down, the difference in height (potential) provides the force. In a circuit, the P.D. is the electrical "height difference."

• Definition: Potential Difference is the work (energy) required per unit charge to move that charge between two points.
  $$V = \frac{W}{Q}$$
• Key Unit: The unit of P.D. is the Volt (\(V\)). One Volt is equivalent to one Joule per Coulomb ($1 \, J C^{-1}$).
• What it means: A potential difference of 12 V across a circuit component means that 12 Joules of electrical energy are converted into other forms of energy (like heat or light) for every 1 Coulomb of charge that passes through the component.

2.2 Electromotive Force (EMF, \(\mathcal{E}\))

The device that provides the energy to start the charge flow (like a battery or power supply) is characterized by its Electromotive Force (EMF), often denoted by \(\mathcal{E}\).

EMF is the total energy supplied by the source per unit charge.

• Analogy: EMF is like the total energy produced by a water pump. P.D. is the energy used up by different parts of the plumbing system (resistors).
• Key Difference: EMF is the potential difference measured across the terminals of a source when no current is being drawn from it (i.e., the circuit is open). When current is drawn, some energy is lost inside the source due to Internal Resistance, and the P.D. across the terminals will be slightly less than the EMF.

Section 3: Resistance, Ohm’s Law, and Energy Transfer

3.1 Defining Resistance (R)

When charges move through a material, they constantly collide with the atoms and ions in the lattice structure. These collisions convert the electrical energy into thermal energy (heat). This opposition to current flow is called Resistance (\(R\)).

Analogy: If current is traffic flow, resistance is the congestion caused by narrow roads and speed bumps.

• Key Unit: The unit of resistance is the Ohm ($\Omega$).

3.2 Ohm’s Law

Ohm's Law describes the relationship between Voltage, Current, and Resistance for certain materials (Ohmic conductors) at a constant temperature.

• Statement: The current through a conductor between two points is directly proportional to the potential difference across the two points.
  $$V = IR$$
  Mnemonic: Think of a triangle V-I-R to easily rearrange the formula.
• Ohmic vs. Non-Ohmic:
  • Ohmic Conductors: Have a constant resistance ($R$) regardless of the voltage or current (e.g., standard metal wires kept at a constant temperature). Their V-I graph is a straight line through the origin.
  • Non-Ohmic Conductors: Their resistance changes with temperature or voltage (e.g., a filament lamp or a diode). The resistance of a filament lamp increases as it heats up, so the V-I graph curves.

3.3 Resistivity (\(\rho\)): A Particulate View

Why does a thick copper wire have less resistance than a thin iron wire? Resistance depends on the physical dimensions and the material itself.

• Length (\(L\)): The longer the wire, the more collisions, so $R \propto L$.
• Cross-sectional Area (\(A\)): The wider the wire, the more paths for electrons, so $R \propto 1/A$.
• Resistivity (\(\rho\)): This is a property of the material itself, independent of shape. It quantifies how strongly a material resists electric current. Good conductors (like copper) have low resistivity.

The relationship is given by:

$$R = \rho \frac{L}{A}$$

The unit for resistivity ($\rho$) is Ohm-metre ($\Omega \, m$).

3.4 Electrical Energy and Power

Electrical energy is transferred whenever a current flows through a component with a P.D. across it. This energy is often dissipated as heat or light.

• Power (P): Power is the rate at which electrical energy (\(W\)) is converted into other forms (Work done per unit time).
  $$P = \frac{W}{t}$$
• Power Formulas: Combining \(P = W/t\), \(W = VQ\), and \(I = Q/t\), we get the core power relationship:
  $$P = VI$$
• Alternative Power Formulas (using Ohm's Law, \(V=IR\)):
  $$P = I^2 R$$ $$P = \frac{V^2}{R}$$
• Energy (E): Since $P = E/t$, electrical energy consumed is $E = P t$. The unit of energy is the Joule (\(J\)), but household electricity often uses the kilowatt-hour (kWh).

Section 4: Circuit Analysis and Components

4.1 Circuit Diagrams and Symbols

To analyze circuits, we use standardized symbols:

• Cell/Battery (DC Source): Provides constant EMF.
• Resistor: Component used to introduce resistance.
• Switch: Controls the flow of current (open or closed).
• Ammeter: Measures current (A).
• Voltmeter: Measures potential difference (V).

4.2 Measuring Devices

It is vital to know how to connect measuring devices correctly:

Ammeters (Measuring Current):

To measure the flow through a point, the ammeter must be placed in series with the component. An ideal ammeter has zero resistance so it does not affect the current being measured.

Voltmeters (Measuring Potential Difference):

To measure the energy drop across a component, the voltmeter must be placed in parallel with the component. An ideal voltmeter has infinite resistance so that no current flows through it, ensuring it only measures the potential difference.

4.3 Resistors in Series

A series circuit provides only one path for the current to flow. Components are connected end-to-end.

Analogy: A single line of traffic.

1. Current (I): The current is the same everywhere.
   $$I_{total} = I_1 = I_2 = I_3$$
2. Potential Difference (V): The total voltage supplied is shared among the components.
   $$V_{total} = V_1 + V_2 + V_3$$
3. Total Resistance (\(R_S\)): The total resistance is the sum of individual resistances. Adding resistors in series increases the total resistance.
   $$R_{S} = R_1 + R_2 + R_3 + ...$$

4.4 Resistors in Parallel

A parallel circuit provides multiple paths (branches) for the current to flow. The components are connected across the same two points.

Analogy: Multiple cash registers or toll booths.

1. Potential Difference (V): The voltage across each parallel branch is the same.
   $$V_{total} = V_1 = V_2 = V_3$$
2. Current (I): The total current splits up to flow through the different branches and recombines afterwards. The path with the least resistance gets the most current.
   $$I_{total} = I_1 + I_2 + I_3$$
3. Total Resistance (\(R_P\)): The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. Adding resistors in parallel decreases the total resistance.
   $$\frac{1}{R_{P}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$$

✨ Engagement Feature: Why Parallel is Better at Home

In your house, all appliances are wired in parallel. Why? If they were in series, turning off one light would break the circuit, turning off everything else! Plus, in parallel, every device gets the full line voltage (e.g., 230 V), ensuring they operate at their designed brightness/power.