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.

Charging Materials

1. Charging by Friction: When you rub two different insulating materials together (like a balloon on hair), you create an imbalance of charge.

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.

2. Charging by Induction (Supplement Content): A conductor can be charged without direct contact using a charged rod and an earth connection:

  1. Bring a charged rod (e.g. negatively charged) close to an uncharged, insulated metal conductor. Electrons in the conductor are repelled to the far side.
  2. Touch the conductor with a finger or wire to earth it; electrons flow away to earth.
  3. Remove the earth connection while holding the charged rod in place.
  4. Remove the charged rod. The conductor is left with an induced positive charge distributed across its surface.
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. Around a Charged Conducting Sphere: Field lines are perpendicular (radial) to the surface, pointing outwards for a positively charged sphere and inwards for a negatively charged sphere.

4. Between Parallel Plates (Oppositely Charged): The field lines are parallel and uniformly spaced, pointing from the positive plate to the negative plate (ignoring edge 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 connected in series with the component.

  • Analogue Meters: Use a pointer across a graduated scale. Readings require reading from the correct scale and avoiding parallax error.
  • Digital Meters: Display values directly on a digital screen, reducing human reading errors.
  • Ranges: Meters often have multiple ranges (e.g. \(0\text{--}200\text{ mA}\) or \(0\text{--}10\text{ A}\)); select an appropriate range so the reading is precise without exceeding the maximum scale.
Electron Flow vs. Conventional Current (Supplement Content)

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.

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 mains sockets.

Key Takeaway for Current: Current \(I = Q/t\). It is measured by an ammeter connected in series. Conventional current flows from (+) to (-), while electron flow is from (-) to (+).

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

Voltage is measured in Volts (V) using a voltmeter (analogue or digital), 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 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 transferred by the charge as it passes through a component.

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 components.

Key Takeaway for Voltage: E.m.f. is energy supplied per unit charge (source). P.d. is energy transferred 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.

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 \(\mathbf{A}\))

Factors Affecting Resistance (Core & Supplement)

The resistance of a metallic wire depends on three factors:

  1. Length (L): Resistance is directly proportional to length (\(R \propto L\)). A longer wire increases resistance.
  2. Cross-sectional Area (A): Resistance is inversely proportional to cross-sectional area (\(R \propto \frac{1}{A}\)). A thicker wire decreases resistance.
  3. Material: Different materials have different inherent resistivities.

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 (\(R = V/I\)) remains constant.
2. Filament Lamp (Non-Ohmic Conductor)

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

  • As p.d. increases, current increases, making the filament hotter.
  • As temperature increases, lattice ions vibrate more vigorously, resisting electron flow.
  • Result: Resistance increases as temperature and current increase.
3. Diode (Non-Ohmic Conductor)

A diode allows current to flow in one direction only.

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

Determining Resistance Experimentally

We determine the resistance of a component 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 vary current).
  2. Connect a voltmeter (\(V\)) in parallel across the component.
  3. Adjust the variable resistor to record various pairs of \(I\) and \(V\) readings.
  4. Plot a graph of \(V\) against \(I\) or calculate \(R = V/I\).

5. Electrical Energy and Electrical Power (4.2.5)

Electrical circuits transfer energy from a power source to circuit components, which then dissipate it as thermal energy, light, or mechanical work.

Electrical Power (\(P\))

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

In electrical circuits, 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 \(\mathbf{V}\))

Electrical Energy (\(E\))

Since power is energy transferred per unit time (\(P = E/t\)), the total electrical energy transferred is:

\(E = P t = IVt\)

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 domestic electricity consumption, the Joule is too small. Electricity meters measure electrical energy in kilowatt-hours (kWh).

Definition: A kilowatt-hour (kWh) is the electrical energy transferred by a \(1\text{ kW}\) appliance running for \(1\text{ hour}\).

Calculating Cost:

1. Energy used in kWh: \(\text{Energy (kWh)} = P\text{ (kW)} \times t\text{ (h)}\)
2. Total cost: \(\text{Cost} = \text{Energy (kWh)} \times \text{Cost per kWh}\)

Example: A 2 kW heater runs for 3 hours. Energy used = \(2\text{ kW} \times 3\text{ h} = 6\text{ kWh}\). At \$0.10 per kWh, total cost = \(6\text{ kWh} \times \$0.10/\text{kWh} = \$0.60\).

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