JW

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.