Welcome to Electrical Quantities!

Hello! This chapter is the absolute foundation of understanding how electricity works in circuits. We are going to explore the key concepts that govern electric flow, including charge, current, voltage, resistance, and power. Don't worry if these terms seem abstract—we will use simple analogies to make them easy to grasp. Mastering these 'building blocks' is essential for tackling the rest of the Electricity and Magnetism section!

1. Electric Charge (Q) and Electrostatics (4.2.1)

What is Electric Charge?

Everything is made of atoms, and atoms contain tiny charged particles: protons (positive) and electrons (negative).

  • Positive Charge: Caused by a deficit (lack) of electrons.
  • Negative Charge: Caused by an excess (extra) of electrons.

The rules of attraction and repulsion are simple and crucial:

  • Like charges repel: Positive repels Positive; Negative repels Negative.
  • Opposite charges attract: Positive attracts Negative.
Measuring Charge (Supplement Content)

Charge is a fundamental quantity and is measured in units called the coulomb, symbol \(\mathbf{C}\).

Did you know? One coulomb is a huge amount of charge! It takes approximately \(6.24 \times 10^{18}\) electrons to make up 1 C of negative charge.

Electrostatics: Charging by Friction

When you rub two different insulating materials together (like a balloon on hair), you create an imbalance of charge. This is called charging by friction (electrostatics).

Key Concept: When solids are charged by friction, only negative charges (electrons) are transferred. The positive charges (protons) are locked inside the atomic nucleus and cannot move.

Conductors and Insulators

Materials behave differently when electricity is applied:

  1. Electrical Conductors: These materials allow charge (electrons) to flow easily.
  2. Electrical Insulators: These materials resist the flow of charge.

The Electron Model Explanation:
Metals (like copper, gold, iron) are good conductors because they contain free electrons (also called delocalised electrons) that are not tied to any single atom and can move freely throughout the structure.

Insulators (like plastic, rubber, wood) hold their electrons tightly; they have no free electrons, so charge cannot easily pass through them.

Electric Fields (Supplement Content)

An electric field is a region where an electric charge experiences a force.

  • We draw electric field lines to show the direction and strength of this force.
  • The direction of the field at any point is defined as the direction of the force that would act on a small positive charge placed at that point.

Electric Field Patterns:

1. Around a Positive Point Charge: Lines radiate outwards (since a positive test charge would be repelled).

2. Around a Negative Point Charge: Lines radiate inwards (since a positive test charge would be attracted).

3. Between Parallel Plates (Oppositely Charged): The field lines are parallel and uniformly spaced, pointing from the positive plate to the negative plate (ignoring end effects).

Key Takeaway for Charge: Charge is measured in Coulombs (\(C\)). Like charges repel, opposites attract. Friction only transfers electrons. Good conductors have free electrons.

2. Electric Current (I) (4.2.2)

Definition of Current

An electric current (\(I\)) is related to the flow of electric charge (\(Q\)). Simply put, it is the rate of flow of charge.

If you imagine electricity flowing through a wire like water flowing through a pipe, the current is how much water (charge) passes a point every second.

The Current Equation (Supplement Content)

Current is formally defined as the charge passing a point per unit time:

$$I = \frac{Q}{t}$$

Where:

  • \(I\) = Current (measured in amperes, \(\mathbf{A}\))
  • \(Q\) = Charge (measured in coulombs, \(\mathbf{C}\))
  • \(t\) = Time (measured in seconds, \(\mathbf{s}\))
Measuring Current

Current is measured using an ammeter. Ammeters must always be connected in series with the component you are measuring, so that the current flows directly through the meter.

Electron Flow vs. Conventional Current (Supplement Content)

This is a potential tricky area, so pay close attention!

1. Electron Flow (The Reality): In metals, the actual particles carrying the charge are free electrons. Electrons are negative, so they flow from the negative terminal to the positive terminal.

2. Conventional Current (The Convention): Before scientists knew about electrons, they assumed charge flowed from positive to negative. We still use this convention today in circuit diagrams and rules!

Rule to Remember: Conventional current flows from Positive (+) to Negative (-). Electron flow is the opposite.

Analogy: Think of a road sign convention. We might all agree to drive on the right (conventional current), even if the actual cars (electrons) are moving in the opposite direction!

Direct Current (d.c.) vs. Alternating Current (a.c.)

  • Direct Current (d.c.): Charge flows in one direction only. Sources include batteries and electrical cells.
  • Alternating Current (a.c.): Charge flows back and forth, constantly changing direction. This is the type of electricity supplied by the mains (wall sockets) in your home.

Key Takeaway for Current: Current \(I = Q/t\). It is measured by an ammeter connected in series. Remember the direction conflict: conventional current (+) to (-), electrons (-) to (+).

3. Electromotive Force (e.m.f.) and Potential Difference (p.d.) (4.2.3)

Voltage is measured in Volts (V) and is measured using a voltmeter, which is always connected in parallel across the component.

Analogy: The Electric Water Circuit

To understand e.m.f. and p.d., imagine a circuit as a loop of water pipes:

  • The battery is the pump.
  • The current is the flowing water.
  • The components (like a bulb) are water wheels that use the energy.

Electromotive Force (\(E\))

The e.m.f. is the total electrical energy supplied by the source (the pump) to move a unit charge completely around the circuit.

Definition: The electrical work done by a source in moving a unit charge around a complete circuit.

$$E = \frac{W}{Q}$$

Where:

  • \(E\) = e.m.f. (measured in Volts, \(\mathbf{V}\))
  • \(W\) = Work done or Energy supplied (measured in Joules, \(\mathbf{J}\))
  • \(Q\) = Charge (measured in Coulombs, \(\mathbf{C}\))

Potential Difference (p.d.) or Voltage (\(V\))

The p.d. is the energy lost or transferred *by* the charge as it passes *through* a component (the water wheel).

Definition: The work done by a unit charge passing through a component.

$$V = \frac{W}{Q}$$

Where:

  • \(V\) = Potential difference (measured in Volts, \(\mathbf{V}\))
  • \(W\) = Work done or Energy transferred to the component (measured in \(\mathbf{J}\))
  • \(Q\) = Charge (measured in \(\mathbf{C}\))

Quick Note: In a simple circuit, the e.m.f. provided by the source is equal to the total p.d. dropped across all the components.

Key Takeaway for Voltage: E.m.f. is energy *supplied* per unit charge (source). P.d. is energy *transferred* (or lost) per unit charge (component). Both are measured in Volts (\(V\)).

4. Resistance (R) (4.2.4)

Defining Resistance

Resistance is the opposition to the flow of electric current. It converts electrical energy into other forms of energy, usually heat and light (e.g., in a lamp or heater).

Ohm’s Law and the Resistance Equation

Resistance is defined using the relationship between p.d. and current:

$$R = \frac{V}{I}$$

Where:

  • \(R\) = Resistance (measured in ohms, \(\mathbf{\Omega}\))
  • \(V\) = Potential difference (in \(\mathbf{V}\))
  • \(I\) = Current (in \(\mathbf{A}\))

Mnemonic: Think of a grumpy old man saying, Very Important Relationship (V=IR, rearranged to R=V/I).

Factors Affecting Resistance (Core & Supplement)

The resistance of a metallic wire depends on three factors:

  1. Length (L): Resistance is directly proportional to length. A longer wire means electrons have to travel further and encounter more obstacles, increasing resistance.
  2. Cross-sectional Area (A): Resistance is inversely proportional to cross-sectional area. A thicker wire (larger area) provides more space for electrons to flow, decreasing resistance.
  3. Material: Different materials (e.g., copper vs. constantan) have different inherent resistance (a property called resistivity).

Analogy: Think of traffic on a highway. Resistance is high if the highway is long or if it is narrow (small area).

Current-Voltage (I-V) Characteristics (Supplement Content)

We can plot graphs of current (y-axis) against potential difference (x-axis) to understand how different components resist current flow.

1. Constant Resistance Resistor (Ohmic Conductor)

The I-V graph is a straight line passing through the origin.

  • This component obeys Ohm’s Law: \(V\) is directly proportional to \(I\).
  • The resistance (\(R = V/I\)) is constant.
2. Filament Lamp (Non-Ohmic Conductor)

The I-V graph is a curve that bends towards the V-axis.

  • As the p.d. increases, the current increases, making the filament hotter.
  • As temperature increases, the metallic ions vibrate more, making it harder for electrons to pass.
  • Result: The resistance increases as the current increases.
3. Diode (Non-Ohmic Conductor)

A diode is designed to allow current to flow in one direction only.

  • It has very low resistance in the forward direction (above a small threshold voltage) and extremely high (almost infinite) resistance in the reverse direction.

Determining Resistance Experimentally

We determine the resistance of a component (like a wire) by measuring the voltage across it and the current passing through it.

Steps:

  1. Set up a series circuit containing the component, an ammeter (\(A\)), a power supply, and a variable resistor (to control current).
  2. Connect a voltmeter (\(V\)) in parallel across the component.
  3. Adjust the variable resistor to get different values of \(I\) and record the corresponding values of \(V\).
  4. Plot a graph of \(V\) against \(I\).
  5. Calculate resistance \(R\) by finding the gradient of the straight-line graph, or by calculating \(R = V/I\) for each reading.

Quick Review Box: Resistance

| Component | I-V Graph Shape | Resistance (R) | | :--- | :--- | :--- | | Resistor | Straight line through origin | Constant | | Filament Lamp | Curved (bends towards V-axis) | Increases with temperature | | Diode | Allows flow in one direction only | Very high in reverse direction |

5. Electrical Energy and Electrical Power (4.2.5)

Electrical circuits are fundamentally about energy transfer. The source (e.m.f.) provides electrical energy, which is then transferred by components into other forms (heat, light, mechanical energy) and dissipates into the surroundings.

Electrical Power (\(P\))

Power is defined as the rate at which energy is transferred or the rate at which work is done.

In the context of electricity, power is the product of current and potential difference:

$$P = IV$$

Where:

  • \(P\) = Power (measured in watts, \(\mathbf{W}\))
  • \(I\) = Current (in \(\mathbf{A}\))
  • \(V\) = Potential difference (in \(\mathbf{V}\))

Memory Aid: Power is like I Visit appliances to give them energy.

Electrical Energy (\(E\))

Electrical energy transferred depends on the power and how long the component is switched on.

Since power is energy per unit time (\(P = E/t\)), we can rearrange this:

$$E = P t$$

Substituting the power equation \(P = IV\):

$$E = IVt$$

Where:

  • \(E\) = Energy transferred (measured in Joules, \(\mathbf{J}\))
  • \(I\) = Current (in \(\mathbf{A}\))
  • \(V\) = Potential difference (in \(\mathbf{V}\))
  • \(t\) = Time (in seconds, \(\mathbf{s}\))

The Kilowatt-Hour (kWh)

When calculating the cost of electricity usage in your home, the Joule is too small a unit. Electrical companies measure usage in kilowatt-hours (kWh).

Definition: The kilowatt-hour (kWh) is the energy used by a device with a power of 1 kilowatt operating for 1 hour.

This is the unit your electricity bill uses!

Calculating Cost (Step-by-Step):

1. Ensure power (\(P\)) is in kilowatts (\(kW\)) and time (\(t\)) is in hours (\(h\)).
2. Calculate energy used in kWh: $$Energy\ (kWh) = P\ (kW) \times t\ (h)$$ 3. Calculate total cost: $$Cost = Energy\ (kWh) \times \text{Cost per kWh}$$

Example: A 2 kW heater runs for 3 hours. If electricity costs $0.10 per kWh, the energy used is \(2\ kW \times 3\ h = 6\ kWh\). The cost is \(6\ kWh \times \$0.10/kWh = \$0.60\).

Key Takeaway for Power and Energy: Power is the rate of energy transfer (\(P=IV\)). Energy transferred over time is \(E=IVt\). When dealing with household bills, use the kilowatt-hour (kWh).