SL IB Physics Current & Circuits

Circuit Diagrams

• Circuit diagrams use universally recognized symbols to represent electrical components.

Circuit Symbols

• Cells & Batteries:
  • A cell converts chemical energy into electrical energy.
  • Current flow is from the positive (longer side) to the negative (shorter side) terminal, opposite to electron flow.
  • A battery comprises multiple cells.
• Switch:
  • A switch controls circuit continuity, turning it on (closed) or off (open).
• Voltmeters & Ammeters:
  • A voltmeter measures the potential difference between two points.
  • An ammeter measures the current flowing in a circuit.
• Fixed Resistor:
  • A fixed resistor limits current flow, transforming electrical potential energy into other forms like thermal energy.
• Variable Resistor:
  • A variable resistor's resistance can be adjusted, inversely affecting circuit current.
• Light-Dependent Resistor (LDR):
  • LDR resistance varies with light intensity; resistance decreases as light intensity increases, and vice versa.
• Thermistor:
  • Thermistor resistance varies with temperature; resistance decreases as temperature increases, and vice versa.
• Potentiometer:
  • A potentiometer is a resistor with a sliding contact forming an adjustable voltage divider.
• Lamp:
  • A lamp emits light by heating a filament.
• Light-Emitting Diode (LED):
  • An LED emits light when current passes through it in one direction only.
• Heating Element:
  • A heating element converts electrical energy into thermal energy through resistance.
• Motor:
  • A motor converts electrical energy into mechanical energy.
• Earth (Ground):
  • The earth connection provides a low-resistance path for instantaneous discharge in case of malfunction.

Drawing Circuit Diagrams

• Circuit diagrams show component arrangement, essential for proper function.
• A circuit diagram must include:
  • An energy source (cell, battery, or power supply) to provide potential difference.
  • A closed path for continuous electron flow.
  • Electrical components with correct symbols, serving as sensors, measurement tools, or energy converters.

Measuring Current

• Electric current is measured using an ammeter connected in series.
• Ideal ammeters possess zero resistance to avoid altering the measured current.

Measuring Potential Difference

• Potential difference (voltage) is measured using a voltmeter connected in parallel.
• A voltmeter measures the difference in electric potential across a component.
• 1 Volt (V) is equivalent to 1 Joule per Coulomb (J/C).

Key Rules

• Ammeters are connected in series.
• Voltmeters are connected in parallel.
• Current flows from positive to negative terminal.

Electric Current

• Electric current is the rate of flow of charge carriers, measured in amperes (A).
• Charge is measured in coulombs (C).
• Current arises when charged conductors are connected, allowing charge flow.
• Conventional current flows from positive to negative, opposite to electron flow.
• Direct current (dc) flows in one direction, produced by cells and batteries.
• The equation for current is: I = \frac{\Delta q}{\Delta t}, where I is current (A), \Delta q is the change in charge (C), and \Delta t is the time interval (s).

Example

• Finding current in a circuit using I = \frac{\Delta q}{\Delta t}.

Important Considerations

• Conventional current flows from positive to negative.
• Current is a scalar quantity, with the sign indicating direction.
• Direct current flows in one direction.

Electric Potential Difference

• Potential difference (p.d.) measures electrical potential energy transferred by electrons between two points.
• Definition: Work done per unit charge in moving a positive charge between two points.
• Measured in volts (V), calculated as: V = \frac{W}{q}, where V is potential difference (V), W is work done (J), and q is charge (C).
• 1 V = 1 J/C
• Cells and batteries provide potential difference in d.c. circuits
• Electrons gain electrical potential energy moving through a cell.

The Electronvolt

• The electronvolt (eV) is a unit of energy for microscopic particles.
• Definition: Energy needed to move an electron through a potential difference of one volt.

Example

• 1 eV in joules: W = qV = eV = (1.6 × 10^{-19} C) × 1 V = 1.6 × 10^{-19} J

Electrical Conductors & Insulators

Conductors

• Conductors allow charge flow easily.
  • Examples: silver, copper, aluminium, steel.
• Metals are excellent conductors due to delocalized electrons.
• Current is the rate of electron flow.

Insulators

• Insulators have no free charges, impeding charge flow.
  • Examples: rubber, plastic, glass, wood.
• Insulators can conduct static electricity by building up charge.

Electric Resistance

• Electrons collide with metal ions, transferring electrical potential energy, increasing internal energy and causing heating.
• Greater heating effect implies higher resistance.
• Copper has low resistance, making it ideal for wires.
• Ideal voltmeters have infinite resistance; ideal ammeters have zero resistance.

Calculating Resistance

• Resistance R is the ratio of potential difference to current: R = \frac{V}{I}
• Units: ohms (Ω)
• Higher resistance means lower current, and vice versa.
• In SI base units: 1 Ω = 1 kg m² s⁻³ A⁻²

Example

• Calculating resistance: R = \frac{V}{I}

Electrical Resistivity

• Resistance of a sample depends on material, length, and cross-sectional area.
• Resistance is directly proportional to length and inversely proportional to cross-sectional area (\pi r^2).

Resistivity

• Resistivity (ρ) describes a material's opposition to current flow.
• ρ = RA / L, where ρ is resistivity (Ω m), R is resistance (Ω), A is area (m²), and L is length (m).
• Conductors have low resistivity; insulators have high resistivity.

Example

• Comparing resistivity of copper and aluminium to determine the better conductor.

I-V Characteristics

Ohm's Law

• Ohm's law: For a component at constant temperature, current is proportional to potential difference: V = IR
• Ohmic components have a linear current-voltage graph through the origin.
• Fixed resistors are ohmic; filament lamps are non-ohmic.
• Resistance can be calculated from the inverse gradient of I-V graph.

Example

• Determining resistance variation with voltage from a graph.

I-V Characteristics of Common Conductors

• Ohmic conductors: wires (at constant temperature), resistors.
• Non-ohmic conductors: semiconductor diodes (LEDs), filament lamps, thermistors, and LDRs.

I-V Characteristics

• Resistor: I-V graph is a straight line through the origin.
• Semiconductor Diode: Forward-biased shows a sharp current increase; reverse-biased shows zero current.
• Filament Lamp: Behaves ohmically at small voltages but becomes non-ohmic as temperature increases.

Series & Parallel Circuits

Resistors in Series

• Current is the same at any point.
• Potential difference is split across components.
• Total resistance: R = R1 + R2 + R_3

Resistors in Parallel

• Total current is the sum of currents in each branch.
• Potential difference is the same across each loop.
• Total resistance: \frac{1}{R} = \frac{1}{R1} + \frac{1}{R2}

Summary of Rules

• Series: Current is constant; voltages add; resistances add.
• Parallel: Voltage is constant; currents add; reciprocal resistances add.

Example

• Calculating ammeter readings in a combined circuit.
• Calculating voltmeter readings in a combined circuit.

Electrical Power

• Electrical energy dissipates as thermal energy when current works against resistance.
• Heat produced depends on current and resistance.
• Power P is the rate of doing work: P = \frac{E}{t} = \frac{W}{t}
• Electrical power: P = IV
• Using Ohm's Law: P = I^2R = \frac{V^2}{R}
• Energy transferred: E = VIt

Example

• Analyzing lamp brightness in a series circuit.

Sources of Electrical Energy

• Electric cells store chemical energy, converted to electrical energy.
• Types: chemical cells, solar cells, mains electricity, wind generators.

Chemical Cells

• Batteries use chemical reactions.
• Rechargeable vs. non-rechargeable.

Solar Cells

• Photovoltaic cells convert sunlight into electrical energy.

Advantages & Disadvantages

• Each energy source has advantages (high energy density, portability) and disadvantages (pollution, cost).

Electromotive Force & Internal Resistance

Electromotive Force (e.m.f.)

• E.m.f. is chemical energy converted to electrical energy per coulomb of charge.
• Measured in volts (V).
• E.m.f. is the potential difference across a cell when no current flows.

Internal Resistance (r)

• All power supplies have internal resistance, causing energy dissipation and voltage loss.
• A cell can be modeled as an e.m.f. source with internal resistance in series.
• E = I(R + r), where E is e.m.f. (V), I is current (A), R is external resistance (Ω), and r is internal resistance (Ω).

Example

• Calculating current and lost volts in a circuit with internal resistance.

Variable Resistance

Thermistors

• Thermistors are non-ohmic resistors with resistance varying with temperature.
• Most have a negative temperature coefficient (NTC).
• Used in ovens, fire alarms, digital thermometers.

Light-Dependent Resistors (LDR)

• LDRs are non-ohmic resistors with resistance changing with light intensity.
• Used as light sensors in streetlights and garden lights.

Potentiometer

• A potentiometer is a variable resistor used as a potential divider.
• Adjusting the slider changes resistance and output voltage.

Example

• Analyzing the effect of temperature decrease on a thermistor circuit.
• Analyzing the current-voltage relationship in an LDR circuit.