A-Level Physics: Electricity

Electric Current

• Definition: Rate of flow of charge.
• Equation: ( I = \frac{\Delta Q}{\Delta T} )
  • ( I ): Electric current (amps)
  • ( \Delta Q ): Charge (coulombs)
  • ( \Delta T ): Time (seconds)
• Example problem:
  • Given: 5 million coulombs flow in 3 minutes.
  • Solution: ( I = \frac{5 \times 10^{-3}}{3 \times 60} \approx 2.8 \times 10^{-5} ) amps.

Potential Difference

• Definition: Work done per unit charge.
• Equation: ( V = \frac{W}{Q} )
  • ( V ): Potential difference (volts)
  • ( W ): Work done (joules)
  • ( Q ): Charge (coulombs)
• SI Base Unit: ( kg \cdot m^2 \cdot s^{-3} \cdot A^{-1} )
• Example problem:
  • Given: 5 J of energy for 2 coulombs.
  • Solution: ( V = \frac{5}{2} = 2.5 ) volts.

Resistance

• Definition: Potential difference across a conductor divided by current.
• Equation: ( R = \frac{V}{I} )
  • ( R ): Resistance (ohms)
• SI Base Unit: ( kg \cdot m^2 \cdot s^{-3} \cdot A^{-2} )
• Example problem:
  • Resistor of 100 ohms, connected to 50W power supply.
  • Given time: 20 minutes, Charge: 850 coulombs.

Ohm's Law

• Statement: Current is directly proportional to the potential difference across it at constant temperature.
• Equation: ( V = I \times R )
• Graph: Straight line through the origin in an ( I-V ) graph.

IV Characteristics

• Standard Resistor:
  • Graph: Straight line through origin, obeys Ohm's Law.
• Filament Lamp:
  • Graph: Curves, does not obey Ohm's Law.
• Negative Temperature Coefficient Thermistor:
  • Graph: Current increases faster than PD, resistance decreases.
• Semiconductor Diode:
  • Conducts in one direction, high resistance otherwise.

Resistivity

• Equation: ( R = \rho \frac{L}{A} )
  • ( \rho ): Resistivity, material constant.
• SI Unit: ( \Omega \cdot m )
• Example problem:
  • Two resistors, same material, different diameters.
  • Calculate resistance ratio.

Superconductivity

• Definition: Zero resistivity below a critical temperature.
• Applications: Strong magnetic fields, reduced energy loss in power transmission.

Measurement of Resistivity

• Experiment setup: Measure resistance, length, and diameter.
• Tools: Ruler, micrometer.

Electrical Circuits

• Resistors in Series: ( R_{total} = R_1 + R_2 )
• Resistors in Parallel: ( \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} )

Energy and Power Equations

• Power: ( P = \frac{E}{t} = VI )
• Alternative Forms: ( P = I^2R = \frac{V^2}{R} )

Kirchhoff's Laws

• First Law: Sum of currents entering a junction equals sum exiting.
• Second Law: Sum of emfs in a loop equals sum of PDS.

Example Problems

• Current Calculation: Use Kirchhoff's laws for circuit analysis.
• Resistance and Power: Calculate using series/parallel rules.

Potential Dividers

• Definition: Divide voltage into parts with resistors.
• Equation: ( V_{out} = \frac{R_2}{R_1 + R_2} V_{in} )

EMF vs Potential Difference

• EMF: Energy conversion from other forms to electrical.
• PD: Energy conversion from electrical to other forms.

Internal Resistance

• Effect: Causes voltage drop inside the cell.
• Equation: ( E = V + Ir )

Number Density & Drift Velocity

• Number Density: Charge carriers per unit volume.
• Drift Velocity Equation: ( I = nAve )

These notes summarize key concepts and equations in A-Level physics electricity, covering everything from basic current and voltage to more complex topics like internal resistance and Kirchhoff's laws. Use these notes to review and understand how different components and principles interrelate within electrical circuits.