Electricity

Question 1

Conventional Current

Answer 1

Electric Current:

• Defined as the rate of flow of charge carriers.
• Units: Amperes (A) or amps.

Current Flow:

• When two oppositely charged conductors are connected, charge flows between them, creating a current.
• Direction of conventional current: From positive to negative (in metals).

Measuring Current:

• Use an ammeter, always connected in series.
• The current should always be a positive value

Question 2

Conductors and Electrolytes

Answer 2

Electrons in Metals:

• In metals (e.g., copper, mercury, titanium), charge flow is due to electrons.
• Metal ions are arranged in a crystal lattice with delocalised electrons (conduction electrons).
• These free electrons make metals good conductors of electricity.
• When a metal conducts electricity, electrons drift slowly from the negative terminal to the positive terminal, creating a current.

Ions in Electrolytes:

• Ions are atoms that have lost or gained electrons:
  
  • Cations: Positive ions (lost electrons).
  • Anions: Negative ions (gained electrons).
• Electrolytes (e.g., copper sulfate in water) conduct electricity via ions, not electrons.
• Anions are attracted to the anode, and cations to the cathode.

Question 3

Kirchhoff’s First Law

Answer 3

Kirchhoff’s First Law:

• The sum of currents entering a junction equals the sum of currents leaving the junction.
• This is a consequence of the conservation of charge.

Series Circuit:

• The current is the same at any point in the circuit.

Parallel Circuit:

• The current divides at junctions, with each branch having a different current value.
• Kirchhoff’s first law applies at each junction..

Question 4

Current in a Current Carrying Conductor

Answer 4

Charge Carriers and Drift Velocity:

• In conductors, charge carriers are usually free electrons.
• Electrons travel a short distance before colliding with metal ions, resulting in a slow drift velocity (v).
  
  • For positive charge carriers, drift velocity is in the same direction as current.
  • For negative charge carriers (e.g., electrons), drift velocity is in the opposite direction to current.
• Drift velocity is the average velocity of charge carriers (∼ 10⁻³ m s⁻¹).

Current and Number Density:

• Current (I) depends on:
  
  • Number density (n): Number of charge carriers per unit volume.
  • Cross-sectional area (A): A = πr² (r = radius of the wire).
  • Drift velocity (v).
  • Charge of carriers (q): q = e for electrons (-1.60 × 10⁻¹⁹ C).
• Key Relationships:
  
  • v is inversely proportional to n: More charge carriers slow down drift velocity.
  • I is directly proportional to n: More charge carriers increase current. .

Question 5

Conductors, Semiconductors & Insulators

Answer 5

Ohmic Conductors:

• Follow Ohm’s Law
• Have a high number density (n) (∼10²⁸ m⁻³).
• Many free electrons per unit volume, making them good conductors.
• Examples: Copper, aluminium, calcium.

Semiconductors:

• Conductivity is between conductors and insulators.
• Temperature dependence:
  
  • Low temperature: Resistivity increases, conductivity decreases.
  • High temperature: Resistivity decreases, conductivity increases.
• Examples: Silicon, germanium.
• Used in electronic devices (e.g., diodes, transistors).
• Doping: Adding impurities to improve conductivity by increasing n.

Insulators:

• Have a very low number density (n) (close to 0).
• Almost no free electrons, making them poor conductors.
• Examples: Plastic, rubber, glass.
• Used for safety to prevent heat or electricity flow (e.g., plug casings).

Question 6

Diode

Answer 6

• A diode is a component that allows current to flow in one direction only.
• In the correct direction, diodes have a threshold voltage (typically 0.6 V) above which current can flow.

Question 7

Electromotive Force (E.M.F) and Internal Resistance

Answer 7

Electromotive Force (E.M.F):

• Defined as the chemical energy converted to electrical energy per unit charge (C) in a power supply.
• E.m.f. describes the transfer of energy from the power supply to electrical charges within the circuit
• Source: Battery or power supply.
• Equal to the potential difference across the cell when no current is flowing.
• Measured using a high-resistance voltmeter in an open circuit.

Internal Resistance (r):

• All power supplies have internal resistance between their terminals.
• Causes energy loss as charge circulates, making the cell warm over time.
• A cell can be modeled as a source of e.m.f with an internal resistance in series.

Exam Tips:

• If a question states “a battery of negligible internal resistance”, assume e.m.f = terminal p.d.
• If internal resistance is included, use e.m.f equations.

Question 8

Power

Answer 8

Power in Mechanics:

• Defined as the rate of doing work.

Electrical Power:

• Potential difference (V): Work done per unit charge.
• Current (I): Rate of flow of charge.
• Electrical power (P): Energy transferred per second
  
  • Dissipated or produced in a circuit.
  • Calculated as P = V × I.

Question 9

Light-Dependent Resistor

Answer 9

Light-Dependent Resistor (LDR):

• A light-sensitive semiconductor whose resistance decreases as light intensity increases.
• Mechanism: Light energy excites electrons, moving them to the conduction band, reducing resistance.

Resistance Range:

• In the dark: Resistance is very high (millions of ohms).
• In bright light: Resistance is very low (tens of ohms).

Applications:

• Used as light sensors in circuits that automatically switch on lights in low light conditions.
• Examples: Street lighting, garden lights.

Question 10

Negative Temperature Coefficient Thermistor

Answer 10

Thermistor:

• A non-ohmic conductor and sensory resistor whose resistance varies with temperature.
• Most thermistors are Negative Temperature Coefficient (NTC):
  
  • Resistance decreases as temperature increases (and vice versa).

Temperature-Resistance Graph:

• The graph is a curve showing resistance decreasing with increasing temperature.
• Key Exam Tip:
  
  • The graph should not touch the x-axis, as this would imply 0 resistance (only possible in superconductors).

Question 11

Potential Difference

Answer 11

Potential Difference (Voltage):

• Defined as the energy transferred per unit charge flowing through a component.
• Energy transfer: From electrical energy to other forms (e.g., heat, light).
• Units: Volts (V) or Joules per Coulomb (J C⁻¹).
• Example: A bulb with 3 V loses 3 J of energy per coulomb of charge.

Key Point:

• Potential difference describes the loss of energy from charges as electrical energy is converted to other forms.

Measuring Potential Difference:

• Use a voltmeter, always connected in parallel to the component.

Question 12

Resistivity

Answer 12

Resistivity:

• Defined as the resistance of a cube with unit-length sides.
• Units: Ω m (ohm-metres).
• Property of the material, dependent on temperature.

Resistance in Wires:

• Resistance (R) depends on:
  
  • Length (L): Longer wire = greater resistance.
  • Cross-sectional area (A): Thicker wire = smaller resistance.
  • Resistivity (ρ): Higher resistivity = higher resistance.
• Equation: R = ρL / A.

Effect of Temperature:

• As temperature increases:
  
  • Ions vibrate more, causing more collisions with free electrons.
  • Current decreases, so resistance increases.
  • Resistivity increases (since ρ ∝ R if A and L are constant).

Applications:

• Copper is used for wires due to its low resistivity, allowing easy current flow.
• Cross-sectional area: For a circular wire, A ∝ diameter².

Question 13

Kirchhoff’s Second Law

Answer 13

Kirchhoff’s Second Law:

• The sum of e.m.f’s in a closed circuit equals the sum of potential differences.
• This is a consequence of the conservation of energy.

Series Circuit:

• Voltage is split across components based on their resistance.
• The sum of voltages equals the total e.m.f of the power supply.

Parallel Circuit:

• Voltage is the same across each closed loop.
• Each loop acts as an independent series circuit, splitting at junctions.
• Usefulness:
  
  • Commonly used in home wiring systems.
  • If one component (e.g., a light) breaks, others continue to function.

Question 14

Lost Volts and Terminal PD

Answer 14

Terminal Potential Difference (p.d):

• The potential difference across the terminals of a cell.
• Formula: ( V = IR ).
• If there is no internal resistance, terminal p.d equals e.m.f.
• With internal resistance, terminal p.d is always lower than e.m.f.

Lost Volts (v):

• The voltage lost due to internal resistance.
• Formula: v = e.m.f - terminal p.d
• In a closed circuit, current flows through the cell, and lost volts develop across the internal resistance.

Question 15

Potential Divider

Answer 15

Potential Divider

• What it does: Splits input voltage (V_in) into smaller output voltages (V_out) using two resistors in series.

How Does It Work?

1. Basic Setup:
   
   • Two resistors, R₁ and R₂, are connected in series across a power supply.
   • The input voltage (V_in) is applied across the entire circuit.
   • The output voltage (V_out) is measured across one resistor (e.g., R₂).

Key Concepts to Remember

1. Ohm’s Law:
   
   • The voltage across a resistor is proportional to its resistance:
2. Resistance Ratio:
   
   • The resistor with the larger resistance gets a greater share of the voltage.

Exam Tips

• Always ensure the correct resistor is in the numerator of the equation (the one across which V_out is measured) .
• For circuits with variable resistors (e.g., LDRs or thermistors), remember that their resistance changes with external conditions, affecting V_out .

Question 16

Combining Resistors

Answer 16

Resistors in Series:

• The combined resistance is the sum of individual resistances:

Resistors in Parallel:

• The reciprocal of the combined resistance is the sum of reciprocals of individual resistances:
  
  • (1/R _total for resistors in parallel)
• The combined resistance is less than the smallest individual resistance.

Question 17

Cathode

Answer 17

A negatively charged electrode
(Anode being positive)

Question 18

Kilowatt-hour

Answer 18

Kilowatt-Hour (kW h):

• A unit of energy equal to 1 kW of power sustained for 1 hour.
• Conversion: 1 kW h = 1000 W × 3600 s = 3.6 × 10⁶ J.

Electricity Bills:

• Energy usage is measured in kW h.
• Cost is calculated by multiplying the number of units used by the price per unit.

Question 19

Super conductor

Answer 19

• Superconductors exhibit zero resistivity at or below a critical transition temperature, which varies by material.
• Many materials become superconducting at extremely low temperatures, around 10 K (-260°C).

Question 20

How to analyse circuits

Answer 20

Steps to Analyse a Circuit:

1. Calculate Total Resistance (Rₜₒₜₐₗ):
   
   • For series circuits: Rₜₒₜₐₗ = R₁ + R₂ + R₃ + …
   • For parallel circuits: 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + 1/R₃ + …
2. Calculate Total Current (Iₜₒₜₐₗ):
   
   • Use Ohm’s Law: Iₜₒₜₐₗ = emf / Rₜₒₜₐₗ
3. Calculate P.D. Across Each Component:
   
   • For series circuits: P.D. is split based on resistance V = IR
   • For parallel circuits: P.D. is the same across all branches.
4. Calculate Current in Each Branch:
   
   • For parallel circuits: : I_branch = emf / R_branch

Key Definitions:

• Junction: A point where at least three circuit paths meet.
• Branch: A path connecting two junctions.

Tips for Complex Circuits:

• Draw Arrows: Show current flow (from positive to negative) at each junction to avoid confusion.
• Parallel Circuits: Junctions only appear in parallel circuits.

Question 21

Electronvolt (eV)

Answer 21

Electronvolt (eV):

• A unit of energy equal to the work done by an electron accelerated through a potential difference of 1 volt.
• Kinetic energy gained:
  
  • When an electron is accelerated through 1 V, it gains 1 eV of energy. (10 V = 10 eV etc.)
  • Formula: eV = (1/2)mv²

Conversions:

• eV → J: Multiply by 1.6 × 10⁻¹⁹.
• J → eV: Divide by 1.6 × 10⁻¹⁹.

Electron Gun:

• Creates a beam of electrons with specific kinetic energy by applying an accelerating potential difference between an anode and a hot filament.

Question 22

Mains

Answer 22

• AC (alternating voltage)
• 50 Hz 230 V
• AC to DC formula is amplitude ÷ √2

Question 23

Circuits with Multiple Sources of e.m.f

Answer 23

Cells in Series:

• Total voltage is the sum of the potential differences across each cell.

Cells in Parallel:

• Total voltage is the same as for one cell.

Current Direction:

• Current flowing from positive to negative is taken as positive.
• Current flowing in the opposite direction is taken as negative.

Question 24

Charge

Answer 24

Charge (Q or q):

• Unit: Coulomb (C).
• Definition:
  
  • 1 C = quantity of charge passing a point per second when a current of 1 A flows.
  • In SI base units: 1 C = 1 A × 1 s.

Elementary Charge (e):

• Magnitude: e = 1.60 × 10⁻¹⁹ C.
• Charge of an electron: -e = -1.60 × 10⁻¹⁹ C.
• Charge of a proton: +e = +1.60 × 10⁻¹⁹ C.

Quantisation of Charge:

• Charge is quantised, meaning it exists in multiples of e.
• The net charge on a particle is always a multiple of the elementary charge.

Question 25

Resistance

Answer 25

Resistance:

• Defined as the opposition to current.
• Measure of how difficult it is for charge to travel through a material.
• For a given potential difference, higher resistance means lower current.
• Units: Ohms (Ω), where 1 Ω = 1 V A⁻¹.

Question 26

Ohm’s Law

Answer 26

Ohm’s Law:

• For a conductor at constant temperature, current (I) is proportional to potential difference (V).
• Constant temperature implies constant resistance.

Key Points:

• Resistors obey Ohm’s Law; filament lamps do not.
• Metal wires obey Ohm’s Law unless the current increases their temperature.

Question 27

I-V Graphs

Answer 27

Ohmic Conductor:

• I–V graph: A straight line passing through the origin.
• Current (I) is directly proportional to the potential difference (V).
• Resistance (R) is constant and can be calculated as R = V / I.
• Example: Fixed resistor.

Semiconductor Diode:

• I–V graph:
  
  • Forward bias (current flows in the direction of the arrowhead):
    
    • Sharp increase in current and potential difference on the right side of the graph.
  • Reverse bias (diode switched around):
    
    • Zero current or potential difference on the left side, followed by a steep vertical drop.
• LED (Light-Emitting Diode):
  
  • Similar to a diode, but the sharp increase in potential difference occurs at a higher voltage (depending on the frequency of light emitted).

Filament Lamp:

• I–V graph: An ‘S’ shaped curve.
• Explanation:
  
  • As current increases, the filament heats up, increasing its resistance.
  • Higher resistance opposes the current, causing the current to increase at a slower rate.
• Ohm’s Law: Obeyed only for small voltages (where the graph is a straight line).
• Resistance: Increases as the graph curves.

Thermistor:

• I–V graph: A shallow curve upwards.
• Explanation:
  
  • As potential difference increases, current increases, raising the temperature of the thermistor.
  • Higher temperature decreases resistance, allowing even more current to flow.
• Ohm’s Law: Does not obey Ohm’s Law, as current is not directly proportional to potential difference.

Question 28

Potentiometer

Answer 28

Potentiometer:

• A variable resistor that acts as a potential divider, providing a continuously adjustable output voltage.
• Structure: A coil of wire with a sliding contact that divides it into two resistances (upper and lower parts).

How It Works:

1. Sliding Contact:
   
   • Moving it up increases the lower resistance and output voltage (V_out).
   • Moving it down decreases the lower resistance and V_out.

Output Voltage Range:

• Maximum V_out: When the sliding contact is at the top
• Minimum V_out: When the sliding contact is at the bottom

Applications:

1. Comparing Potentials: Measures potential differences in different parts of a circuit.
2. Adjustable Outputs: Used in volume controls, dimmer switches, and other devices requiring variable voltage.