The resistance of a filament lamp increasing with current is a fundamental concept in the study of electricity, particularly under the topics of resistance and resistivity. This phenomenon is integral to the curriculum of the AS & A Level Physics - 9702 board, providing students with insights into the behavior of materials under varying electrical conditions. Understanding this relationship is crucial for applications ranging from everyday lighting solutions to advanced electrical engineering systems.

Key Concepts

Understanding Resistance in Filament Lamps

Resistance is a measure of the opposition that a material offers to the flow of electric current. In the context of filament lamps, resistance plays a pivotal role in determining the lamp's performance and efficiency.

Ohm’s Law and Its Application

Ohm’s Law is a fundamental principle that relates voltage (V), current (I), and resistance (R) in an electrical circuit, expressed as:

$$ V = I \cdot R $$

According to Ohm’s Law, for a given voltage, an increase in current would necessitate a proportional increase in resistance, assuming the temperature remains constant.

Temperature Dependence of Resistance

In filament lamps, the resistance is not constant but varies with temperature. As electrical current flows through the filament, it heats up due to the electrical energy being converted into thermal energy. This rise in temperature affects the resistance:

$$ R = R_0 [1 + \alpha (T - T_0)] $$

Where:

R is the resistance at temperature T.
R₀ is the initial resistance at temperature T₀.
α is the temperature coefficient of resistance.

The temperature coefficient α is positive for metals, meaning resistance increases with temperature.

Filament Materials and Their Properties

Filaments in lamps are typically made from tungsten due to its high melting point and favorable electrical properties. Tungsten’s resistance increases significantly with temperature, making it ideal for producing hot filaments that emit light efficiently.

Power Consumption and Heat Generation

The power consumed by a filament lamp is given by:

$$ P = V \cdot I = I^2 \cdot R $$

As current increases, not only does the power consumption rise, but so does the heat generated, further increasing the filament’s temperature and, consequently, its resistance.

Non-linear Resistance Behavior

Unlike some materials that exhibit linear resistance behavior, filament lamps display non-linear characteristics where resistance increases more rapidly as current rises, primarily due to substantial temperature changes in the filament.

Practical Implications in Electrical Circuits

In practical applications, understanding the increase in resistance with current is essential for designing circuits that manage heat dissipation and ensure the longevity of filament lamps. This knowledge helps in selecting appropriate filament materials and predicting lamp performance under varying electrical loads.

Mathematical Derivation of Resistance Increase

Starting from the basic relationship of resistance and temperature:

$$ R = R_0 [1 + \alpha (T - T_0)] $$

Given that the temperature of the filament increases with the power dissipated:

$$ P = I^2 \cdot R $$

As current (I) increases, power (P) increases, leading to a higher temperature (T), which in turn increases the resistance (R). This creates a feedback loop where increased current leads to higher resistance.

Examples and Applications

Consider a tungsten filament lamp rated at 60W and 120V. Initially, the filament has a resistance:

$$ R_0 = \frac{V^2}{P} = \frac{120^2}{60} = 240 \text{ Ω} $$

When the lamp is operating, the temperature rises, increasing the resistance to, say, 300 Ω. If the voltage increases to 130V, the new current can be calculated as:

$$ I = \frac{V}{R} = \frac{130}{300} \approx 0.433 \text{ A} $$>

This example illustrates how an increase in voltage leads to an increased current, which raises the filament temperature and subsequently its resistance.

Graphical Representation

Graphing resistance against current for a filament lamp typically shows a positive correlation, where resistance increases as current increases, reflecting the temperature dependence of the filament’s resistivity.

Real-World Observations

In practical scenarios, when a filament lamp is turned on, the initial current surge is higher due to the low initial resistance at room temperature. As the filament heats up, resistance increases, stabilizing the current flow and ensuring consistent luminosity.

Factors Affecting Resistance Increase

Material of the Filament: Different materials have varying temperature coefficients of resistance.
Ambient Temperature: External temperatures can influence the filament's operating temperature.
Filament Geometry: The length and cross-sectional area of the filament affect how resistance changes with temperature.

Implications for Energy Efficiency

Understanding the resistance behavior of filament lamps helps in optimizing energy consumption. While higher resistance can lead to more efficient light production, excessive resistance may cause overheating and reduce the lamp’s lifespan.

Limitations of the Filament Lamp Model

While filament lamps provide a clear demonstration of resistance increasing with current, real-world applications may involve additional complexities such as varying ambient conditions and material inconsistencies that can affect resistance in unpredictable ways.

Conclusion of Key Concepts

The resistance of a filament lamp increasing with current is a direct consequence of temperature rise in the filament material. This behavior is governed by fundamental principles of electricity and material science, and it has significant practical implications for the design and operation of electrical devices utilizing filament lamps.

Advanced Concepts

Thermal Runaway in Filament Lamps

Thermal runaway is a phenomenon where an increase in temperature leads to a further increase in resistance, which in turn causes more heat generation. In filament lamps, this can lead to a self-limiting effect where resistance rises to a point that stabilizes current flow, preventing excessive temperatures that could otherwise cause the filament to fail.

Mathematical Modeling of Resistance Change

To model the resistance change in filament lamps, we consider both electrical and thermal equations. Combining Ohm’s Law with the temperature dependence of resistance, we derive a more comprehensive equation:

$$ R(T) = R_0 \left(1 + \alpha \left(\frac{P}{k} - T_0\right)\right) $$>

Where:

k is the thermal conductivity of the filament material.
P is the power dissipated.
T₀ is the ambient temperature.

This equation allows for predicting resistance changes based on power input and material properties.

Non-Ohmic Behavior and Its Implications

Filament lamps exhibit non-Ohmic behavior because their resistance is not constant but varies with temperature and current. This deviations from Ohm’s Law have important implications for circuit design, requiring engineers to consider dynamic resistance values in their calculations.

Quantum Considerations in Resistivity

At higher temperatures, electron-phonon interactions become significant, affecting the resistivity of the filament material. Quantum mechanics provides a deeper understanding of these interactions, explaining how electrons scatter more frequently as atomic vibrations increase with temperature, leading to higher resistance.

Impact of Alloying on Filament Resistance

Alloying tungsten with other elements can alter its temperature coefficient of resistance. For instance, adding carbon or rhenium improves the filament’s performance by enhancing its tensile strength and modifying its resistivity characteristics, thereby allowing for higher operating temperatures and better efficiency.

Advanced Material Science in Filament Production

Modern filament production techniques involve precise control of material composition and filament geometry to optimize resistance behavior. Innovations in nanotechnology and material engineering continue to enhance filament performance, enabling longer-lasting and more efficient lamps.

Energy Band Theory and Resistivity

Energy band theory explains how electrons occupy energy states in materials. In conductors like tungsten, electrons can move freely, but as temperature increases, more electrons occupy higher energy states, increasing scattering events and thus resistivity.

AC vs. DC Effects on Filament Resistance

Alternating current (AC) and direct current (DC) can affect filament resistance differently. AC causes continuous fluctuations in current direction, leading to periodic heating and cooling cycles, whereas DC results in a steady increase in temperature. These differences can influence the overall resistance behavior and filament lifespan.

Environmental Factors Influencing Resistance

External environmental conditions, such as humidity and atmospheric pressure, can impact filament resistance. Moisture can lead to oxidation of the filament material, altering its resistive properties, while varying pressure can affect heat dissipation rates.

Filament Lifetime and Resistance Degradation

Over time, filament lamps experience resistance degradation due to factors like evaporation of filament material, deposition on the glass envelope, and structural fatigue. Monitoring resistance changes can provide insights into the remaining lifespan and performance of the lamp.

Interdisciplinary Connections: Electrical Engineering Applications

The principles governing resistance changes in filament lamps are applicable in various electrical engineering domains. For example, incandescent heating elements, incandescent bulbs in automotive lighting, and diagnostic tools in material science all rely on understanding and managing resistance variations with current and temperature.

Case Study: Design Optimization of a Headlamp

In automotive headlamp design, engineers must optimize filament resistance to ensure adequate brightness while minimizing energy consumption and heat generation. By applying the concepts of resistance increase with current, designers can balance these factors to achieve efficient and reliable headlamp performance.

Future Trends in Lighting Technology

Advancements in lighting technology, such as the shift towards LED and OLED systems, are influenced by the limitations of filament lamps. Understanding resistance behavior in traditional filament lamps informs the development of new materials and technologies that offer superior energy efficiency and longer lifespans.

Experimental Techniques for Measuring Resistance Changes

Accurate measurement of resistance changes in filament lamps involves techniques like four-point probe measurements and temperature-controlled environments. These methods ensure precise data collection, facilitating the analysis and understanding of resistance behavior under varying current conditions.

The Role of Surface Oxidation in Resistance Dynamics

Surface oxidation can significantly impact the resistance of filament materials. Oxidation layers can act as insulators, increasing overall resistance and affecting the filament’s thermal and electrical performance. Controlling oxidation is essential for maintaining consistent resistance behavior.

Integration with Smart Electrical Systems

Smart electrical systems incorporate sensors and feedback mechanisms to monitor and adjust filament resistance in real-time. This integration enhances energy efficiency, ensures optimal performance, and extends the lifespan of filament-based lighting solutions.

Conclusion of Advanced Concepts

Diving deeper into the resistance behavior of filament lamps reveals a complex interplay of thermal, electrical, and material science principles. Advanced theoretical models, interdisciplinary applications, and ongoing technological advancements underscore the importance of comprehensively understanding how resistance increases with current in filament lamps.

Comparison Table

Aspect	Constant Resistance Materials	Filament Lamps
Resistance Behavior	Remains constant with varying current	Increases as current increases
Temperature Dependence	Minimal effect on resistance	Significant increase in resistance with temperature
Material Examples	Resistors, nichrome coils	Tungsten filaments
Applications	Electronic circuits, precision devices	Incandescent lamps, heating elements
Power Consumption	Predictable and stable	Variable with current-induced resistance
Efficiency	High in specific applications	Lower due to heat loss
Lifespan	Typically longer under stable conditions	Shorter due to thermal stress and material evaporation

Summary and Key Takeaways

Resistance in filament lamps increases with current due to temperature rise.
Tungsten’s high temperature coefficient is crucial for filament performance.
Non-linear resistance behavior impacts practical circuit design and lamp efficiency.
Advanced concepts include thermal runaway, quantum effects, and material science innovations.
Understanding resistance dynamics is essential for optimizing lighting technologies.

Examiner Tip

Tips

Remember the mnemonic "HOT FILAMENT RESISTS MORE" to recall that as the filament heats up, its resistance increases. When solving problems, always account for the temperature rise by considering the temperature coefficient. Practice by calculating both cold and operating resistances to strengthen your understanding and ensure accuracy in exams.

Did You Know

Did you know that tungsten filaments can withstand temperatures up to around 3,422°C, making them perfect for efficient light emission? Additionally, the first practical incandescent bulb was invented by Thomas Edison in 1879, utilizing the principle of increasing resistance with current to produce light. Modern advancements have further enhanced filament durability, enabling longer-lasting bulbs used in various high-temperature applications.

Common Mistakes

Students often mistakenly apply Ohm’s Law by assuming resistance remains constant, ignoring its temperature dependence in filament lamps. Another common error is confusing the initial and operating resistances, leading to incorrect current calculations. For example, using the cold resistance of a filament to determine operating current results in inaccurate predictions.

FAQ

Why does the resistance of a filament lamp increase with current?

As current flows through the filament, it heats up due to electrical energy conversion. The rise in temperature increases the atomic vibrations in the filament material, leading to greater opposition to electron flow and thus higher resistance.

How does Ohm’s Law apply to filament lamps?

Ohm’s Law ($V = I \cdot R$) applies to filament lamps by relating voltage, current, and resistance. However, since the resistance changes with temperature, the relationship becomes non-linear, requiring adjustments for accurate calculations under operating conditions.

What is the role of the temperature coefficient of resistance in filament lamps?

The temperature coefficient of resistance ($\alpha$) quantifies how much the resistance of the filament material changes with temperature. A positive $\alpha$ indicates that resistance increases as temperature rises, which is essential for the functioning of filament lamps.

Why is tungsten commonly used for filament lamps?

Tungsten is used because of its high melting point, excellent thermal stability, and favorable electrical properties. These characteristics allow tungsten filaments to withstand high temperatures without melting, ensuring efficient and long-lasting light emission.

How does filament resistance affect the brightness of a lamp?

Higher resistance in the filament reduces the current flow for a given voltage, which can decrease brightness. Conversely, as resistance increases with temperature, it stabilizes the current, maintaining consistent luminosity despite initial surges.

What are common applications of filament lamps beyond lighting?

Beyond lighting, filament lamps are used as heating elements in devices like toasters and ovens, in automotive headlamps, and in scientific instruments where controlled heat generation is required.

1. Capacitance

1.1 Energy Stored in a Capacitor

1.1.1 Determine electric potential energy stored in a capacitor from the area under the potential–charge g

1.1.2 Recall and use W = ½QV = ½CV²

1.2 Discharging a Capacitor

1.2.1 Analyze graphs of potential difference, charge, and current during capacitor discharge

1.2.2 Recall and use τ = RC for the time constant during discharge

1.2.3 Use equations of the form x = x₀e^(-t / RC) for current, charge, or potential during discharge

1.3 Capacitors and Capacitance

1.3.1 Define capacitance for isolated spherical conductors and parallel plate capacitors

1.3.2 Recall and use C = Q / V

1.3.3 Derive formulae for combined capacitance of capacitors in series and parallel

1.3.4 Use capacitance formulae for capacitors in series and parallel

2. Nuclear Physics

2.1 Mass Defect and Nuclear Binding Energy

2.1.1 Sketch the variation of binding energy per nucleon with nucleon number

2.1.2 Explain nuclear fusion and nuclear fission

2.1.3 Calculate the energy released in nuclear reactions using E = c²∆m

2.1.4 Understand the equivalence between energy and mass (E = mc²)

2.1.5 Define and use the terms mass defect and binding energy

2.2 Radioactive Decay

2.2.1 Understand that fluctuations in count rate provide evidence for random decay

2.2.2 Understand that radioactive decay is spontaneous and random

2.2.3 Define activity and decay constant, and recall A = λN

2.2.4 Define half-life

2.2.5 Use λ = 0.693 / t₁/₂ for the half-life relationship

2.2.6 Understand exponential decay and use the relationship x = x₀e^(-λt)

3. Kinematics

3.1 Equations of Motion

3.1.1 Define and use distance, displacement, speed, velocity, acceleration

3.1.2 Use graphical methods to represent motion

3.1.3 Determine displacement from velocity–time graph

3.1.4 Determine velocity using gradient of displacement–time graph

3.1.5 Determine acceleration using gradient of velocity–time graph

3.1.6 Derive equations for uniformly accelerated motion

3.1.7 Solve problems of uniformly accelerated motion

3.1.8 Describe experiment to determine acceleration due to gravity

3.1.9 Explain motion with uniform velocity and perpendicular acceleration

4. Deformation of Solids

4.1 Stress and Strain

4.1.1 Understand and use the terms load, extension, compression, and limit of proportionality

4.1.2 Recall and use Hooke’s law

4.1.3 Recall and use the formula for spring constant k = F / x

4.1.4 Define and use terms stress, strain, and Young's modulus

4.1.5 Describe an experiment to determine Young’s modulus

4.1.6 Understand deformation caused by tensile or compressive forces

4.2 Elastic and Plastic Behaviour

4.2.1 Understand elastic and plastic deformation and elastic limit

4.2.2 Understand area under the force–extension graph as work done

4.2.3 Calculate elastic potential energy using EP = ½kx²

5. Gravitational Fields

5.1 Gravitational Field of a Point Mass

5.1.1 Understand that g is approximately constant for small height changes near Earth's surface

5.1.2 Recall and use g = GM / r²

5.1.3 Derive and use g = GM / r² for gravitational field strength

5.2 Gravitational Potential

5.2.1 Define gravitational potential as work done per unit mass in bringing a test mass from infinity

5.2.2 Use ϕ = -GM / r for gravitational potential due to a point mass

5.2.3 Use EP = -GMm / r for gravitational potential energy between two point masses

5.3 Gravitational Field

5.3.1 Define gravitational field as force per unit mass

5.3.2 Represent a gravitational field using field lines

5.4 Gravitational Force Between Point Masses

5.4.1 For point outside uniform sphere, treat mass as a point mass at its center

5.4.2 Analyze circular orbits in gravitational fields

5.4.3 Recall and use Newton's law of gravitation F = Gm₁m₂ / r²

6. Electricity

6.1 Resistance and Resistivity

6.1.1 Understand that the resistance of a thermistor decreases as temperature increases

6.1.2 Define resistance and recall and use V = IR

6.1.3 Sketch I–V characteristics for metallic conductor, semiconductor diode, and filament lamp

6.1.4 Explain that the resistance of a filament lamp increases as current increases

6.1.5 State Ohm’s law and recall and use R = ρL / A

6.1.6 Understand that the resistance of an LDR decreases as light intensity increases

6.2 Electric Current

6.2.1 Understand that an electric current is a flow of charge carriers

6.2.2 Understand that the charge on charge carriers is quantised

6.2.3 Recall and use Q = It

6.2.4 Use I = Anvq for current-carrying conductors

6.3 Potential Difference and Power

6.3.1 Define potential difference as energy transferred per unit charge

6.3.2 Recall and use V = W / Q

6.3.3 Recall and use P = VI, P = I²R, P = V² / R

7. D.C. Circuits

7.1 Practical Circuits

7.1.1 Recall and use the circuit symbols in the syllabus

7.1.2 Draw and interpret circuit diagrams using circuit symbols

7.1.3 Define electromotive force (e.m.f.) of a source as energy transferred per unit charge

7.1.4 Distinguish between e.m.f. and potential difference (p.d.)

7.1.5 Understand the effects of internal resistance on terminal potential difference

7.2 Kirchhoff’s Laws

7.2.1 Recall Kirchhoff’s first law: conservation of charge

7.2.2 Recall Kirchhoff’s second law: conservation of energy

7.2.3 Derive the formula for combined resistance of resistors in series using Kirchhoff’s laws

7.2.4 Use the formula for combined resistance of resistors in series

7.2.5 Derive the formula for combined resistance of resistors in parallel using Kirchhoff’s laws

7.2.6 Use the formula for combined resistance of resistors in parallel

7.2.7 Use Kirchhoff’s laws to solve simple circuit problems

7.3 Potential Dividers

7.3.1 Understand the principle of a potential divider circuit

7.3.2 Recall and use the principle of the potentiometer for comparing potential differences

7.3.3 Understand the use of a galvanometer in null methods

7.3.4 Explain the use of thermistors and LDRs in potential dividers to provide a potential dependent on te

8. Thermal Equilibrium

8.1 Thermal Energy Transfer

8.1.1 Understand that thermal energy transfers from higher to lower temperature

8.1.2 Understand that regions of equal temperature are in thermal equilibrium

9. Temperature Scales

9.1 Temperature Measurement

9.1.1 Understand physical properties that vary with temperature (e.g., density, gas volume, resistance)

9.1.2 Convert temperatures between Kelvin and Celsius, and recall T(K) = θ(°C) + 273.15

10. Magnetic Fields

10.1 Concept of a Magnetic Field

10.1.1 Understand that a magnetic field is a field of force produced by moving charges or permanent magnets

10.1.2 Represent a magnetic field using field lines

10.2 Force on a Current-Carrying Conductor

10.2.1 Understand that a force acts on a current-carrying conductor in a magnetic field

10.2.2 Recall and use F = BIL sin θ for the force on a current-carrying conductor in a magnetic field

10.2.3 Define magnetic flux density as the force per unit current per unit length on a wire at right angles

10.3 Force on a Moving Charge

10.3.1 Determine the direction of the force on a charge moving in a magnetic field

10.3.2 Recall and use F = BQv sin θ for the force on a moving charge in a magnetic field

10.3.3 Understand the origin of the Hall voltage and use the expression VH = BI / (ntq) for the Hall voltag

10.3.4 Understand the use of a Hall probe to measure magnetic flux density

10.4 Magnetic Fields Due to Currents

10.4.1 Sketch magnetic field patterns due to currents in a straight wire, flat coil, and solenoid

10.4.2 Understand that magnetic field in a solenoid is increased by a ferrous core

10.4.3 Explain the origin of forces between current-carrying conductors and determine the direction of the

10.5 Electromagnetic Induction

10.5.1 Define magnetic flux as the product of magnetic flux density and area perpendicular to flux directio

10.5.2 Recall and use Φ = BA for magnetic flux

10.5.3 Understand and use the concept of magnetic flux linkage

10.5.4 Explain experiments that show changing magnetic flux induces an e.m.f.

10.5.5 Recall and use Faraday’s and Lenz’s laws of electromagnetic induction

11. Specific Heat Capacity and Latent Heat

11.1 Specific Heat Capacity

11.1.1 Define and use specific heat capacity

11.2 Latent Heat

11.2.1 Define and use specific latent heat; distinguish between fusion and vaporisation

12. Dynamics

12.1 Momentum and Newton’s Laws of Motion

12.1.1 Mass resists change in motion

12.1.2 Recall F = ma and solve related problems

12.1.3 Define and use linear momentum

12.1.4 Force as rate of change of momentum

12.1.5 State and apply Newton’s laws

12.1.6 Describe weight as effect of gravitational field

12.1.7 Weight of an object is mass × gravitational acceleration

12.2 Non-uniform Motion

12.2.1 Understand frictional and drag forces

12.2.2 Describe motion in uniform gravitational field with air resistance

12.2.3 Objects moving against resistive force may reach terminal velocity

12.3 Linear Momentum and its Conservation

12.3.1 State conservation of momentum

12.3.2 Apply conservation of momentum to solve problems

12.3.3 For elastic collision, kinetic energy and relative speed are conserved

12.3.4 Momentum is conserved, but some kinetic energy may change

13. Medical Physics

13.1 Production and Use of Ultrasound

13.1.1 Understand that a piezo-electric crystal changes shape when a p.d. is applied and generates an e.m.f

13.1.2 Understand how ultrasound waves are generated and detected by a piezoelectric transducer

13.1.3 Understand how ultrasound reflection at boundaries provides diagnostic information about internal st

13.1.4 Define specific acoustic impedance as Z = ρc

13.1.5 Use the equation IR / I₀ = (Z₁ – Z₂)² / (Z₁ + Z₂)² for the intensity reflection coefficient

13.2 Production and Use of X-rays

13.2.1 Explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum

13.2.2 Understand the use of X-rays in imaging internal body structures and the term 'contrast' in X-ray im

13.2.3 Recall and use I = I₀e^(-μx) for the attenuation of X-rays in matter

13.2.4 Understand how computed tomography (CT) produces 3D images by combining multiple 2D X-ray images

13.3 PET Scanning

13.3.1 Understand that a tracer contains radioactive nuclei and is introduced into the body for imaging

13.3.2 Understand that β+ decay is used in positron emission tomography (PET)

13.3.3 Understand that annihilation occurs when a particle interacts with its antiparticle, conserving mass

13.3.4 Explain how gamma-ray photons from annihilation are detected to create an image of tracer concentrat

14. Waves

14.1 Progressive Waves

14.1.1 Describe wave motion in ropes, springs, and ripple tanks

14.1.2 Understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelengt

14.1.3 Use time-base and y-gain on a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

14.1.4 Derive and use v = f λ for the wave equation

14.1.5 Recall and use v = f λ

14.1.6 Understand energy transfer by a progressive wave

14.1.7 Recall and use intensity = power / area, intensity ∝ (amplitude)²

14.2 Transverse and Longitudinal Waves

14.2.1 Compare transverse and longitudinal waves

14.2.2 Analyze and interpret graphical representations of transverse and longitudinal waves

14.3 Doppler Effect for Sound Waves

14.3.1 Understand the change in frequency when a sound source moves relative to a stationary observer

14.3.2 Use the expression f₀ = fₛ(v / (v ± vₛ)) for the observed frequency

14.4 Electromagnetic Spectrum

14.4.1 State all electromagnetic waves are transverse waves traveling at the same speed in free space

14.4.2 Recall the range of wavelengths from radio waves to γ-rays

14.4.3 Recall that wavelengths 400–700 nm are visible to the human eye

14.5 Polarisation

14.5.1 Understand that polarisation is a phenomenon associated with transverse waves

14.5.2 Recall and use Malus's law (I = I₀ cos²θ) to calculate intensity of a plane-polarised wave after pas

15. The Mole

15.1 The Mole

15.1.1 Understand that amount of substance is an SI base quantity with the unit mol

15.1.2 Use molar quantities where one mole contains Avogadro's constant of particles

16. Equation of State

16.1 Ideal Gas Law

16.1.1 Understand that a gas obeying pV ∝ T is an ideal gas

16.1.2 Recall and use the equation pV = nRT for an ideal gas

16.1.3 Recall pV = NkT, where N = number of molecules and k is Boltzmann constant

16.1.4 Use the relationship k = R / NA

17. Kinetic Theory of Gases

17.1 Kinetic Theory

17.1.1 State the basic assumptions of the kinetic theory of gases

17.1.2 Explain pressure exerted by a gas due to molecular movement

17.1.3 Derive and use pV = (3/2)NmkT for pressure of a gas

17.1.4 Compare pV = (3/2)NmkT with pV = NkT to deduce average kinetic energy of a molecule

18. Particle Physics

18.1 Atoms, Nuclei and Radiation

18.1.1 Infer the existence and small size of the nucleus from α-particle scattering

18.1.2 Describe the nuclear atom model: protons, neutrons, and electrons

18.1.3 Distinguish between nucleon number and proton number

18.1.4 Understand isotopes as forms of the same element with different neutrons

18.1.5 Use the notation AZX for nuclides representation

18.1.6 Understand conservation of nucleon number and charge in nuclear processes

18.1.7 Describe the composition, mass, and charge of α-, β-, and γ-radiations

18.1.8 Understand antiparticles and positrons as antiparticles of electrons

18.1.9 State that (electron) antineutrinos are produced during β- decay and neutrinos during β+ decay

18.1.10 Represent α- and β-decay using radioactive decay equations

18.1.11 Use unified atomic mass unit (u) for mass

18.2 Fundamental Particles

18.2.1 Understand quarks as fundamental particles with six flavours

18.2.2 Understand hadrons as baryons (three quarks) or mesons (one quark and one antiquark)

18.2.3 Describe changes in quark composition during β- and β+ decay

18.2.4 Describe protons and neutrons as composed of quarks

18.2.5 Recall and use the charge of each quark and its respective antiquark

18.2.6 Recall electrons and neutrinos as fundamental particles (leptons)

19. Internal Energy

19.1 Internal Energy

19.1.1 Understand that internal energy is the sum of kinetic and potential energies of molecules in a syste

19.1.2 Relate rise in temperature to an increase in internal energy

20. Forces, Density and Pressure

20.1 Turning Effects of Forces

20.1.1 Weight acts at a single point: centre of gravity

20.1.2 Define and apply the moment of a force

20.1.3 Understand the concept of a couple

20.1.4 Define and apply torque of a couple

20.2 Equilibrium of Forces

20.2.1 State and apply the principle of moments

20.2.2 System in equilibrium has no resultant force or torque

20.2.3 Use a vector triangle to represent coplanar forces in equilibrium

20.3 Density and Pressure

20.3.1 Define and use density

20.3.2 Define and use pressure

20.3.3 Derive equation for hydrostatic pressure ∆p = ρg∆h

20.3.4 Use the equation ∆p = ρg∆h

20.3.5 Understand upthrust as the effect of hydrostatic pressure

20.3.6 Calculate upthrust using F = ρgV (Archimedes' principle)

21. Astronomy and Cosmology

21.1 Standard Candles

21.1.1 Understand luminosity as the total power radiated by a star

21.1.2 Recall and use the inverse square law F = L / (4πd²) for radiant flux intensity

21.1.3 Understand that an object with known luminosity is a standard candle

21.1.4 Use standard candles to determine distances to galaxies

21.2 Stellar Radii

21.2.1 Recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the surface temperature of a star

21.2.2 Use Stefan–Boltzmann law L = 4πσr²T⁴

21.2.3 Use Wien’s law and Stefan–Boltzmann law to estimate the radius of a star

21.3 Hubble’s Law and Big Bang Theory

21.3.1 Understand redshift and the increase in wavelength of light from distant objects

21.3.2 Use ∆λ / λ = ∆f / f = v / c for redshift

21.3.3 Explain why redshift suggests the Universe is expanding

21.3.4 Recall and use Hubble’s law v = H₀d to explain the Big Bang theory

22. First Law of Thermodynamics

22.1 First Law

22.1.1 Recall and use W = p∆V for work done when the volume of a gas changes at constant pressure

22.1.2 Understand the difference between work done by a gas and work done on a gas

22.1.3 Recall and use the first law of thermodynamics: ∆U = q + W

23. Alternating Currents

23.1 Characteristics of Alternating Currents

23.1.1 Understand and use terms period, frequency, and peak value for alternating current or voltage

23.1.2 Use x = x₀ sin(ωt) for sinusoidal alternating current or voltage

23.1.3 Recall that the mean power in a resistive load is half the maximum power for sinusoidal current

23.1.4 Distinguish between root-mean-square (r.m.s.) and peak values and recall I₀r.m.s = I₀ / √2 and V₀r.m

23.2 Rectification and Smoothing

23.2.1 Distinguish graphically between half-wave and full-wave rectification

23.2.2 Explain the use of a single diode for half-wave rectification

23.2.3 Explain the use of four diodes (bridge rectifier) for full-wave rectification

23.2.4 Analyze the effect of a capacitor in smoothing, including the effect of capacitance and load resista

24. Superposition

24.1 Stationary Waves

24.1.1 Explain and use the principle of superposition

24.1.2 Understand experiments demonstrating stationary waves using microwaves, stretched strings, and air c

24.1.3 Explain the formation of stationary waves using graphical methods and identify nodes and antinodes

24.1.4 Determine wavelength from the positions of nodes or antinodes

24.2 Diffraction

24.2.1 Explain diffraction and show understanding of related experiments

24.2.2 Understand the effect of gap width relative to wavelength in diffraction experiments

24.3 Interference

24.3.1 Understand the terms interference and coherence

24.3.2 Demonstrate two-source interference using water waves, sound, light, and microwaves

24.3.3 Understand the conditions required for two-source interference fringes

24.3.4 Recall and use λ = ax / D for double-slit interference with light

24.4 Diffraction Grating

24.4.1 Recall and use d sin θ = nλ for diffraction grating calculations

24.4.2 Describe the use of a diffraction grating to determine the wavelength of light

25. Simple Harmonic Oscillations

25.1 Simple Harmonic Motion

25.1.1 Understand and use terms displacement, amplitude, period, frequency, angular frequency, and phase di

25.1.2 Understand that simple harmonic motion occurs when acceleration is proportional to displacement from

25.1.3 Use a = -ω²x and recall x = x₀ sin(ωt) as the solution

25.1.4 Use v = v₀ cos(ωt) and v = ±ω√(x₀² - x²) for velocity

26. Energy in Simple Harmonic Motion

26.1 Energy in SHM

26.1.1 Describe the interchange between kinetic and potential energy during SHM

26.1.2 Recall and use E = ½mω²x₀² for the total energy of a system undergoing SHM

27. Quantum Physics

27.1 Energy and Momentum of a Photon

27.1.1 Understand that electromagnetic radiation has a particulate nature

27.1.2 Recall and use E = hf for the energy of a photon

27.1.3 Use the electronvolt (eV) as a unit of energy

27.1.4 Understand that a photon has momentum and use p = E / c for photon momentum

27.2 Photoelectric Effect

27.2.1 Understand that photoelectrons are emitted from a metal surface when illuminated by electromagnetic

27.2.2 Understand and use the terms threshold frequency and threshold wavelength

27.2.3 Explain photoelectric emission in terms of photon energy and work function

27.2.4 Recall and use hf = Φ + ½mv² for the maximum kinetic energy of photoelectrons

27.2.5 Explain why the maximum kinetic energy of photoelectrons is independent of intensity, while current

27.3 Wave-Particle Duality

27.3.1 Understand that the photoelectric effect shows the particulate nature of light, while diffraction sh

27.3.2 Describe and interpret electron diffraction as evidence for the wave nature of particles

27.3.3 Understand the de Broglie wavelength as the wavelength associated with a moving particle

27.3.4 Recall and use λ = h / p for de Broglie wavelength

27.4 Energy Levels in Atoms and Line Spectra

27.4.1 Understand discrete electron energy levels in atoms (e.g., atomic hydrogen)

27.4.2 Understand the appearance and formation of emission and absorption line spectra

27.4.3 Recall and use hf = E₁ – E₂ for the energy difference between electron energy levels

28. Damped and Forced Oscillations, Resonance

28.1 Damped Oscillations

28.1.1 Understand that damping occurs due to resistive forces

28.1.2 Understand the types of damping: light, critical, and heavy damping

28.2 Resonance

28.2.1 Understand that resonance occurs when an oscillating system is forced to oscillate at its natural fr

29. Work, Energy and Power

29.1 Energy Conservation

29.1.1 Understand the concept of work, and recall W = F × s

29.1.2 Apply the principle of conservation of energy

29.1.3 Understand efficiency as useful energy output / total energy input

29.1.4 Use efficiency concept to solve problems

29.1.5 Define power as work done per unit time

29.1.6 Solve problems using P = W / t

29.1.7 Derive P = Fv and solve problems

29.2 Gravitational Potential Energy and Kinetic Energy

29.2.1 Derive ∆EP = mg∆h for gravitational potential energy changes

29.2.2 Recall and use ∆EP = mg∆h for gravitational potential energy changes

29.2.3 Derive EK = ½mv² for kinetic energy

29.2.4 Recall and use EK = ½mv² for kinetic energy

30. Electric Fields

30.1 Electric Fields and Field Lines

30.1.1 Understand that an electric field is a field of force and define it as force per unit positive charg

30.1.2 Represent an electric field using field lines

30.2 Uniform Electric Fields

30.2.1 Recall and use E = ∆V / ∆d to calculate electric field strength between charged parallel plates

30.2.2 Describe the effect of a uniform electric field on the motion of charged particles

30.3 Electric Force Between Point Charges

30.3.1 Understand that, for a point outside a spherical conductor, the charge may be considered a point mas

30.3.2 Recall and use Coulomb’s law F = Q₁Q₂ / (4πε₀r²) for the force between two point charges

30.4 Electric Field of a Point Charge

30.4.1 Recall and use E = Q / (4πε₀r²) for the electric field strength due to a point charge

30.5 Electric Potential

30.5.1 Define electric potential as work done per unit positive charge in bringing a test charge from infin

30.5.2 Recall and use V = Q / (4πε₀r) for electric potential due to a point charge

30.5.3 Understand how electric potential leads to electric potential energy of two point charges and use EP

31. Physical Quantities and Units

31.1 Physical Quantities

31.1.1 Physical quantities consist of magnitude and unit

31.1.2 Estimate physical quantities from the syllabus

31.2 SI Units

31.2.1 SI base units: mass, length, time, current, temperature

31.2.2 Express derived units from SI base units

31.2.3 Check homogeneity of physical equations

31.2.4 Use prefixes (pico, nano, micro, kilo, etc.)

31.3 Errors and Uncertainties

31.3.1 Understand systematic and random errors

31.3.2 Assess uncertainty in derived quantities

31.4 uniform Electric Fields

31.4.1 Distinguish between precision and accuracy

31.5 Scalars and Vectors

31.5.1 Difference between scalar and vector quantities

31.5.2 Add and subtract coplanar vectors

31.5.3 Represent a vector as components

32. Motion in a Circle

32.1 Centripetal Acceleration

32.1.1 Understand centripetal acceleration and its role in circular motion

32.1.2 Recall and use a = rω² and a = v² / r

32.1.3 Recall and use F = mrω² and F = mv² / r

32.1.4 Understand force causing centripetal acceleration is always perpendicular to motion

32.2 Kinematics of Uniform Circular Motion

32.2.1 Recall and use ω = 2π / T and v = rω

32.2.2 Understand and use angular speed

32.2.3 Define and express angular displacement in radians

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Introduction