1. Physical Quantities, Units & Measurement
A physical quantity is anything that can be measured, such as length, mass or time. Quantities that do not depend on any other quantity are called fundamental (base) quantities; quantities obtained by combining them are called derived quantities. India follows the SI system (Système International), adopted internationally in 1960.
| Base Quantity | SI Unit | Symbol |
|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
| Derived Quantity | SI Unit | Derived Quantity | SI Unit |
|---|
| Force | newton (N) | Electric charge | coulomb (C) |
| Work / Energy | joule (J) | Potential difference | volt (V) |
| Power | watt (W) | Resistance | ohm (Ω) |
| Pressure | pascal (Pa) | Capacitance | farad (F) |
| Frequency | hertz (Hz) | Magnetic field | tesla (T) |
| Momentum | kg·m/s | Magnetic flux | weber (Wb) |
| Power of a lens | dioptre (D) | Radioactivity | becquerel (Bq) |
| Heat | joule (J) | Luminous flux | lumen (lm) |
Special Units of Length, Mass & Others (frequently asked)
- Light year = distance travelled by light in one year ≈ 9.46 × 1015 m. It is a unit of distance, not time.
- Astronomical Unit (AU) = mean Earth–Sun distance ≈ 1.496 × 1011 m (about 15 crore km).
- Parsec ≈ 3.26 light years — the largest practical unit of distance.
- Angstrom (Å) = 10−10 m (used for wavelength of light); fermi = 10−15 m (size of nucleus); micron = 10−6 m.
- Nautical mile = 1852 m (used in sea and air navigation); knot = one nautical mile per hour (speed of ships).
- Quintal = 100 kg; metric tonne = 1000 kg; carat = 200 mg (for gems).
- 1 horsepower (HP) = 746 W; 1 calorie = 4.18 J; 1 kWh = 3.6 × 106 J; 1 atmosphere = 1.013 × 105 Pa.
Measuring Instruments — the most repeated NTPC table
| Instrument | Measures / Used for | Instrument | Measures / Used for |
|---|
| Ammeter | Electric current (connected in series) | Voltmeter | Potential difference (connected in parallel) |
| Galvanometer | Detects small current | Barometer | Atmospheric pressure |
| Hygrometer | Relative humidity | Hydrometer | Relative density of liquids |
| Lactometer | Purity (density) of milk | Manometer | Pressure of gases |
| Altimeter | Altitude (in aircraft) | Anemometer | Wind speed |
| Seismograph | Earthquake waves | Pyrometer | Very high temperature (furnaces) |
| Odometer | Distance travelled by a vehicle | Speedometer | Instantaneous speed of a vehicle |
| Tachometer | Rotation speed (RPM) of engine shafts | Fathometer | Depth of the sea |
| Sphygmomanometer | Blood pressure | Stethoscope | Heart and lung sounds |
| Audiometer | Hearing ability | Calorimeter | Quantity of heat |
| Rain gauge (Pluviometer) | Rainfall | Thermostat | Keeps temperature constant (fridge, iron) |
| Clinical thermometer | Body temperature (range 35–42 °C) | Screw gauge / Vernier caliper | Very small lengths / diameters |
| SONAR | Locates underwater objects using ultrasound | RADAR | Locates aircraft/objects using radio waves |
🧠 Memory Hook
“Hygro = humidity (both have ‘h’ and water), Hydro = liquid density, Lacto = milk (lactose), Sphygmo = pulse/BP, Anemo = wind (Greek anemos).”
2. Motion
An object is in motion when its position changes with time with respect to a reference point. Motion is relative — a passenger sitting in a moving train is at rest relative to the train but in motion relative to the platform.
Scalar vs Vector
- Scalar: only magnitude — distance, speed, mass, time, work, energy, temperature.
- Vector: magnitude + direction — displacement, velocity, acceleration, force, momentum, weight.
- Distance can never be less than the magnitude of displacement; displacement can be zero even when distance is not (e.g., one complete round of a circular track).
Speed, Velocity, Acceleration
- Speed = distance / time (m/s). 1 km/h = 5/18 m/s.
- Velocity = displacement / time.
- Acceleration = change in velocity / time (m/s²). Negative acceleration = retardation.
- Uniform circular motion has constant speed but changing velocity (direction changes), so it is accelerated motion.
Equations of motion (uniform acceleration):
v = u + at s = ut + ½at² v² = u² + 2as
Average speed for equal distances at speeds x and y = 2xy / (x + y)
Graphs — what the slope and area tell you
- Slope of distance–time graph = speed. A straight line parallel to the time axis means the body is at rest.
- Slope of velocity–time graph = acceleration; area under a velocity–time graph = displacement.
📌 Solved Example (NTPC type)
A train starting from rest attains 72 km/h in 20 s. Acceleration = ? → 72 km/h = 72 × 5/18 = 20 m/s. a = (20 − 0)/20 = 1 m/s². Distance covered = ½ × 1 × 20² = 200 m.
3. Force & Newton’s Laws of Motion
A force is a push or pull that can change the state of rest or motion of a body, or change its shape. Balanced forces do not change the state of motion; unbalanced forces produce acceleration.
Newton’s Three Laws
- First law (Law of Inertia): A body continues in its state of rest or uniform motion in a straight line unless an external unbalanced force acts on it. Inertia depends on mass — greater mass, greater inertia. Galileo first gave the idea of inertia.
- Second law: Rate of change of momentum is proportional to the applied force: F = ma. 1 newton = force that gives 1 kg mass an acceleration of 1 m/s².
- Third law: To every action there is an equal and opposite reaction. Action and reaction act on different bodies, so they never cancel each other.
| Type of Inertia | Everyday Example |
|---|
| Inertia of rest | Passengers fall backward when a bus starts suddenly; dust falls when a carpet is beaten |
| Inertia of motion | Passengers fall forward when a moving bus stops suddenly; an athlete runs before a long jump |
| Inertia of direction | Passengers lean outward when a car takes a sharp turn; mud flies off a rotating wheel tangentially |
Momentum & Its Conservation
- Momentum p = mass × velocity (vector, unit kg·m/s).
- Law of conservation of momentum: If no external force acts, total momentum of a system remains constant. Examples: recoil of a gun, flight of a rocket, a swimmer pushing water backward.
- Impulse = Force × time = change in momentum. A cricketer pulls hands back while catching a ball to increase time and reduce force; vehicles have shock absorbers; high jumpers land on sand/foam — all use the same idea.
Friction
- Friction opposes relative motion between surfaces. Order: static > sliding > rolling friction.
- Friction is reduced by lubricants (oil, grease), ball bearings, streamlined shapes and polishing; increased by treads on tyres and grooves on shoe soles.
- Fluid friction (drag) acts on objects moving through air or water; birds, fish and aeroplanes have streamlined bodies to reduce it.
Circular Motion Forces
- Centripetal force acts towards the centre and keeps a body on a circular path (F = mv²/r). For the Moon around Earth, gravity provides it.
- Centrifugal force is an apparent outward force felt in a rotating frame; used in a cream separator and in the drier of a washing machine.
- Roads and railway tracks are banked (outer edge raised) on curves so that vehicles can turn safely.
4. Gravitation
Universal Law of Gravitation: F = G m₁m₂ / r² G = 6.67 × 10⁻¹¹ N·m²/kg²
Acceleration due to gravity on Earth's surface g ≈ 9.8 m/s² Weight W = mg
Key Facts on g, Mass and Weight
- G is a universal constant (same everywhere); g changes from place to place.
- g is maximum at the poles and minimum at the equator (Earth is slightly flattened at the poles and it rotates).
- g decreases with height above the surface and also with depth below it; at the centre of the Earth, g = 0, so weight becomes zero but mass stays the same.
- Mass is the quantity of matter (scalar, measured by a beam/physical balance, never changes). Weight is the force of gravity on the body (vector, measured by a spring balance, changes with g).
- g on the Moon is about 1/6 of that on Earth, so a 60 kg person weighs as much as a 10 kg mass would weigh on Earth.
- In free fall, all bodies fall with the same acceleration irrespective of mass (Galileo). In vacuum, a feather and a coin fall together.
- A person in a lift feels heavier when the lift accelerates upward and lighter when it accelerates downward; in a freely falling lift the person feels weightless. Astronauts in an orbiting spacecraft feel weightless for the same reason.
Kepler’s Laws of Planetary Motion
- Planets move in elliptical orbits with the Sun at one focus.
- The line joining a planet and the Sun sweeps equal areas in equal times — so a planet moves fastest when nearest the Sun.
- The square of the time period is proportional to the cube of the mean distance from the Sun (T² ∝ r³).
| Satellite Fact | Value |
|---|
| Escape velocity from Earth | 11.2 km/s (Moon: about 2.4 km/s — one reason the Moon has no atmosphere) |
| Orbital velocity of a satellite close to Earth’s surface | about 7.9 km/s |
| Height of a geostationary satellite | about 36,000 km above the equator |
| Time period of a geostationary satellite | 24 hours (same as Earth’s rotation, moves west to east) |
| Uses of geostationary satellites | Communication, TV broadcast, weather (e.g., INSAT/GSAT series) |
| Polar / Sun-synchronous satellites | Lower orbits; used for remote sensing and mapping |
5. Pressure, Buoyancy & Properties of Fluids
Pressure = Force / Area (SI unit: pascal = N/m²)
Liquid pressure at depth h: P = h ρ g Density ρ = mass / volume
Pressure in Daily Life
- Small area → large pressure: knives, needles and nails are sharp; a camel’s broad feet, wide tyres of trucks, broad school-bag straps and railway sleepers spread force over a large area to reduce pressure.
- Liquid pressure increases with depth, so a dam wall is made thicker at the base; deep-sea divers need special suits.
- Atmospheric pressure at sea level = 76 cm of mercury = 1.013 × 105 Pa. It decreases with altitude — the reason for nose-bleeding at high mountains and why fountain pens leak in aircraft. The mercury barometer was invented by Torricelli.
- A sudden fall in barometer reading indicates a storm; a gradual fall indicates rain; a gradual rise indicates fair weather.
- Cooking takes longer on mountains because lower pressure lowers the boiling point of water; a pressure cooker raises pressure and hence the boiling point (to about 120 °C).
Pascal’s Law
Pressure applied to an enclosed liquid is transmitted equally in all directions. Applications: hydraulic lift, hydraulic brakes, hydraulic press, car jacks.
Archimedes’ Principle & Floatation
- A body immersed in a fluid experiences an upward force (buoyant force / upthrust) equal to the weight of the fluid displaced.
- A body floats if its density is less than that of the liquid; it sinks if its density is greater.
- An iron nail sinks but an iron ship floats because the ship’s hollow shape displaces a large volume of water.
- It is easier to swim in sea water than in river water because sea water is denser (higher buoyant force).
- Ice floats on water because ice is less dense than water; about 9/10 of an iceberg remains below the surface.
- Relative density = density of substance / density of water (no unit). Measured by a hydrometer.
Surface Tension
- Property by which a liquid surface behaves like a stretched membrane.
- Raindrops and mercury drops are spherical (a sphere has minimum surface area).
- Insects walk on water; a greased needle floats.
- Soap and detergents reduce surface tension and help in cleaning; surface tension decreases with rise in temperature.
Capillarity & Viscosity
- Capillary action: rise of liquid in a narrow tube — kerosene rising in a lamp wick, ink absorbed by blotting paper, water rising in soil.
- Mercury shows capillary fall.
- Viscosity is the internal friction of a fluid; honey and glycerine are more viscous than water. Viscosity of liquids decreases on heating.
Bernoulli’s Principle (qualitative)
Where the speed of a flowing fluid is high, its pressure is low. It explains the lift of an aeroplane wing, roofs being blown off in storms, a sprayer/atomiser, and why two boats moving side by side are pulled towards each other.
6. Work, Energy & Power
Work W = F × s × cosθ (unit joule; zero if force is perpendicular to displacement)
Kinetic energy KE = ½mv² Potential energy PE = mgh
Power P = W / t (unit watt) 1 HP = 746 W 1 kWh = 3.6 × 10⁶ J
Key Concepts
- No work is done when a coolie stands holding a load on his head, or when a satellite moves in a circular orbit (force perpendicular to motion).
- If velocity is doubled, kinetic energy becomes four times; if mass is doubled, KE doubles.
- Law of conservation of energy: energy can neither be created nor destroyed, only converted from one form to another. For a freely falling body, KE + PE remains constant.
- Energy stored in a stretched rubber band, a wound spring or a raised hammer is potential energy.
- The commercial unit of electrical energy is the kilowatt-hour (kWh), called one “unit” on the electricity bill.
| Device | Energy Conversion |
|---|
| Electric motor / fan | Electrical → Mechanical |
| Generator / dynamo | Mechanical → Electrical |
| Electric bulb | Electrical → Light + Heat |
| Solar cell | Light (solar) → Electrical |
| Dry cell / battery (discharging) | Chemical → Electrical |
| Battery being charged | Electrical → Chemical |
| Microphone | Sound → Electrical |
| Loudspeaker | Electrical → Sound |
| Steam engine / car engine | Heat (chemical) → Mechanical |
| Photosynthesis | Light → Chemical |
7. Heat & Temperature
Heat is a form of energy that flows from a hotter body to a colder body (SI unit joule; older unit calorie). Temperature is the degree of hotness or coldness and decides the direction of heat flow (SI unit kelvin).
| Scale | Ice point | Steam point | Divisions |
|---|
| Celsius (°C) | 0 | 100 | 100 |
| Fahrenheit (°F) | 32 | 212 | 180 |
| Kelvin (K) | 273.15 | 373.15 | 100 |
C/5 = (F − 32)/9 = (K − 273)/5
−40 °C = −40 °F (the only temperature equal on both scales)
Normal body temperature: 37 °C = 98.6 °F = 310 K Absolute zero = 0 K = −273.15 °C
Specific Heat & Latent Heat
- Specific heat capacity = heat needed to raise the temperature of 1 kg of a substance by 1 °C. Water has a very high specific heat (about 4200 J/kg°C). That is why water is used in car radiators and hot-water bags, and why coastal areas have a moderate climate.
- Latent heat is absorbed or released during a change of state without change in temperature. Latent heat of fusion of ice ≈ 3.34 × 105 J/kg; latent heat of vaporisation of water ≈ 22.6 × 105 J/kg.
- Burns from steam at 100 °C are more severe than from boiling water at 100 °C, because steam also gives up its large latent heat.
- Ice at 0 °C cools a drink better than water at 0 °C because ice absorbs latent heat while melting.
Evaporation, Boiling & Humidity
- Evaporation takes place at all temperatures and only from the surface; it causes cooling. It increases with higher temperature, larger surface area, wind speed and lower humidity.
- Examples of cooling by evaporation: water in an earthen pot (matka) stays cool, sweating cools the body, we feel cold after applying spirit/acetone, cotton clothes are preferred in summer.
- Boiling point of water falls when pressure decreases (hills) and rises when impurities like salt are dissolved.
- Humid weather feels sticky because sweat does not evaporate easily.
Thermal Expansion
- Most substances expand on heating. Gaps are left between railway rails, telephone wires are left loose in summer, and bridges have roller supports for this reason.
- Anomalous expansion of water: water contracts when heated from 0 °C to 4 °C; it has maximum density at 4 °C. This is why lakes freeze from the top and aquatic life survives in winter below the ice.
- A bimetallic strip (two metals, e.g., brass and iron) bends on heating — used in thermostats and fire alarms.
| Mode of Heat Transfer | Medium | Examples |
|---|
| Conduction | Mainly solids; particles pass energy to neighbours without moving | Metal spoon gets hot in tea; cooking pans have wooden/plastic handles |
| Convection | Liquids and gases; heated fluid itself moves | Sea breeze (day) and land breeze (night); ventilators near the ceiling |
| Radiation | No medium needed; travels at the speed of light | Heat from the Sun reaching Earth; warmth near a fire |
Good to know
- Silver is the best conductor of heat among metals; air, wood, wool and glass wool are poor conductors (insulators).
- Dark and rough surfaces are good absorbers and good emitters of radiation; white and shiny surfaces are poor absorbers — so white clothes are preferred in summer.
- A thermos flask (Dewar flask) reduces conduction and convection by a vacuum and radiation by silvered walls.
- Greenhouse effect: glass lets short-wave sunlight in but traps long-wave heat radiation.
8. Waves & Sound
A wave carries energy from one place to another without the transfer of matter. Sound is a mechanical wave — it needs a medium (solid, liquid or gas) and cannot travel through vacuum. In air, sound travels as longitudinal waves made of compressions and rarefactions.
Wave Terms
- Wavelength (λ): distance between two consecutive compressions (or crests).
- Frequency (f): number of vibrations per second (hertz).
- Time period T = 1/f.
- Speed v = f × λ.
- Transverse waves: particles vibrate perpendicular to wave direction (waves on a string, light).
Characteristics of Sound
- Loudness depends on amplitude; measured in decibels (dB). Sounds above about 80–85 dB are harmful over time.
- Pitch depends on frequency; a woman’s or child’s voice has higher pitch than a man’s.
- Quality (timbre) depends on waveform; it lets us recognise a person or instrument by voice.
| Medium | Approx. speed of sound |
|---|
| Air (0 °C) | about 332 m/s |
| Air (20–25 °C) | about 343–346 m/s |
| Water | about 1500 m/s |
| Iron / Steel | about 5000–5900 m/s |
Rules to Remember
- Speed of sound: solids > liquids > gases.
- Speed of sound in air increases with temperature and humidity (sound travels faster in moist air). It does not depend on pressure at constant temperature.
- We see lightning before hearing thunder because light (3 × 108 m/s) is far faster than sound.
- An echo is heard only if the reflecting surface is at least about 17.2 m away (the sensation of sound lasts 0.1 s in our ears).
- Reverberation (persistence of sound due to repeated reflections) is reduced in auditoriums using curtains, carpets and sound-absorbing panels.
| Range | Frequency | Heard / used by |
|---|
| Infrasonic | Below 20 Hz | Elephants, whales; produced by earthquakes (before the main shock) |
| Audible | 20 Hz – 20,000 Hz | Human beings |
| Ultrasonic | Above 20,000 Hz | Bats, dolphins, dogs (partly); used in SONAR, ultrasound scanning, cleaning, detecting cracks in metals, breaking kidney stones |
Applications & Terms
- SONAR (Sound Navigation And Ranging) uses ultrasound to find depth of the sea and locate submarines. Bats navigate by echolocation using ultrasound.
- Doppler effect: apparent change in frequency when the source and listener move relative to each other — the whistle of an approaching train sounds shriller. Also used in radar speed guns.
- Supersonic speed = faster than sound; a jet crossing the speed of sound produces a sonic boom. Speed of an object divided by speed of sound = Mach number.
- Stethoscope works on multiple reflection of sound; megaphones and horns also use reflection of sound.
9. Light — Reflection
Light is a form of energy that enables us to see. It travels in straight lines (rectilinear propagation), as transverse electromagnetic waves, and does not need a medium. Speed of light in vacuum = 3 × 108 m/s; sunlight takes about 8 minutes 20 seconds to reach Earth.
Laws of Reflection & Plane Mirror
- Angle of incidence = angle of reflection; incident ray, reflected ray and normal lie in the same plane.
- Image in a plane mirror is virtual, erect, same size, as far behind the mirror as the object is in front, and laterally inverted (that is why “AMBULANCE” is written in mirror form on ambulances).
- To see your full image, a plane mirror must be at least half your height.
- Two plane mirrors at angle θ form (360/θ) − 1 images; at 90° → 3 images; parallel mirrors → infinite images. A kaleidoscope and a periscope use plane mirrors.
Spherical mirrors: f = R/2 Mirror formula 1/v + 1/u = 1/f Magnification m = −v/u
| Mirror | Nature of image | Uses |
|---|
| Concave (converging) | Mostly real and inverted; virtual, erect and enlarged when object is between pole and focus | Shaving and make-up mirrors, dentist’s mirror, reflectors of torches and vehicle headlights, solar cookers/furnaces |
| Convex (diverging) | Always virtual, erect and diminished | Rear-view mirrors of vehicles (wide field of view), street-light reflectors, security mirrors in shops |
10. Light — Refraction, Lenses, Human Eye & Natural Phenomena
Refraction is the bending of light when it passes obliquely from one medium to another because its speed changes. Light bends towards the normal when entering a denser medium (air → glass) and away from the normal when entering a rarer medium.
Refractive index n = speed of light in vacuum / speed of light in medium
Water ≈ 1.33 Glass ≈ 1.5 Diamond ≈ 2.42 (highest among common materials)
Lens formula 1/v − 1/u = 1/f Power P = 1/f (f in metres), unit dioptre (D)
Convex lens: +ve power Concave lens: −ve power
Everyday Refraction
- A pool or tank appears shallower than it is; a stick dipped in water appears bent; letters under a glass slab appear raised.
- Stars twinkle due to atmospheric refraction (changing air layers); planets do not twinkle because they are closer and appear as extended sources.
- The Sun is visible about 2 minutes before actual sunrise and 2 minutes after actual sunset due to atmospheric refraction.
- Mirage in deserts and on hot roads is due to refraction plus total internal reflection.
Total Internal Reflection (TIR)
When light goes from a denser to a rarer medium at an angle greater than the critical angle, it is completely reflected back. Examples: sparkling of diamond (very small critical angle, about 24°), optical fibres used in telecommunication and endoscopy, mirage, and the shining of an air bubble in water.
| Lens | Nature | Uses |
|---|
| Convex (converging) | Thicker at the middle; forms real images (and a virtual, magnified image when object is within focus) | Magnifying glass, camera, projector, microscope and telescope objectives, correcting hypermetropia, human eye lens |
| Concave (diverging) | Thinner at the middle; always virtual, erect, diminished image | Correcting myopia, peepholes in doors |
Human Eye & Its Defects
Parts of the Eye
- Cornea — transparent front bulge; most refraction occurs here; can be transplanted/donated.
- Iris — coloured part; controls the size of the pupil (pupil widens in dim light).
- Eye lens — convex, flexible; ciliary muscles change its focal length (this is called power of accommodation).
- Retina — screen where a real and inverted image forms. Rods work in dim light; cones detect colour. The blind spot (where the optic nerve leaves) has no rods or cones.
- Near point of a normal eye = 25 cm; far point = infinity.
- Persistence of vision ≈ 1/16 second — the basis of movies and animation.
| Defect | Problem | Cause | Correction |
|---|
| Myopia (near-sightedness) | Cannot see distant objects clearly | Eyeball elongated / lens too converging; image forms in front of retina | Concave lens |
| Hypermetropia (far-sightedness) | Cannot see nearby objects clearly | Eyeball too short / lens less converging; image forms behind retina | Convex lens |
| Presbyopia | Difficulty in near vision with age | Weakening of ciliary muscles | Bifocal lens |
| Astigmatism | Blurred vision in one direction | Irregular curvature of cornea | Cylindrical lens |
| Cataract | Cloudy vision | Eye lens becomes opaque | Surgery (lens replaced) |
Dispersion & Scattering of Light
- Dispersion: splitting of white light into seven colours (VIBGYOR) by a prism. Violet deviates the most, red the least. Newton first showed that white light is made of seven colours.
- A rainbow forms by dispersion, refraction and internal reflection of sunlight in raindrops; it is always seen in the direction opposite to the Sun.
- Scattering: smaller wavelengths (blue) scatter much more than longer ones (red). Hence the sky appears blue; the Sun looks reddish at sunrise and sunset (blue light is scattered away over the long path).
- Red is used for danger signals because it scatters the least and can be seen from far away, even in fog.
- To an astronaut in space, the sky appears dark/black because there is no atmosphere to scatter light.
- Clouds look white because the water droplets are large enough to scatter all colours almost equally.
- Tyndall effect: scattering of light by colloidal particles (beam of sunlight in a dusty room or in a forest canopy).
| Primary colours of light | Mixing result |
|---|
| Red + Green | Yellow |
| Green + Blue | Cyan (peacock blue) |
| Red + Blue | Magenta |
| Red + Green + Blue | White |
Electromagnetic Spectrum (increasing wavelength)
Gamma rays → X-rays → Ultraviolet → Visible light (violet to red) → Infrared → Microwaves → Radio waves.
- X-rays (discovered by Wilhelm Röntgen, 1895) are used to see bones.
- UV rays cause sunburn and help the skin make vitamin D; most UV from the Sun is absorbed by the ozone layer.
- Infrared = heat radiation; used in TV remotes and night-vision devices.
- Microwaves are used in microwave ovens and radar; radio waves in radio and TV broadcasting.
11. Electricity
Current I = Q / t (ampere) 1 A = 1 C/s Charge of an electron = 1.6 × 10⁻¹⁹ C
Ohm's law V = IR (at constant temperature) Resistance R = ρL / A
Series: R = R₁ + R₂ + R₃ (same current)
Parallel: 1/R = 1/R₁ + 1/R₂ + 1/R₃ (same voltage)
Power P = VI = I²R = V²/R Heat produced (Joule's law) H = I²Rt
Resistance — What It Depends On
- R increases with length and decreases with area of cross-section (thick wires have less resistance).
- Resistivity (ρ) depends only on the material and temperature, not on dimensions. Resistance of metals increases with temperature.
- Good conductors: silver (best), copper, aluminium, gold. Copper and aluminium are used for household and transmission wires.
- Nichrome (alloy of nickel and chromium) has high resistivity and a high melting point — used in heaters, irons and toasters.
- Tungsten (melting point about 3400 °C) is used for bulb filaments; bulbs are filled with inert gases such as argon or nitrogen to prolong filament life.
- Semiconductors like silicon and germanium are used in diodes, transistors, chips and solar cells. Superconductors have zero resistance at very low temperatures.
Household Electricity in India
- Supply is AC at 220 V and 50 Hz (USA uses 110–120 V, 60 Hz).
- Wire colours (old convention): live — red, neutral — black, earth — green. (New convention: brown, light blue, green-yellow.)
- All household appliances are connected in parallel so each gets the full 220 V and can be switched independently.
- A fuse is a safety device connected in series with the live wire; its wire is made of an alloy with a low melting point (traditionally tin–lead). It melts during overloading or a short circuit. Modern homes use MCBs (Miniature Circuit Breakers).
- Earthing protects users from electric shock by sending leakage current to the ground; appliances with metal bodies (iron, fridge, geyser) must be earthed.
- Short circuit: live and neutral wires touch directly; resistance becomes almost zero and current becomes very high.
📌 Electricity Bill — Solved Example
A 100 W bulb runs 10 hours a day for 30 days. Energy = 100 × 10 × 30 = 30,000 Wh = 30 kWh (30 units). At ₹5 per unit, cost = ₹150.
Two 6 Ω resistors: series = 12 Ω; parallel = 3 Ω. Tip: n equal resistors R in parallel give R/n.
12. Magnetism & Magnetic Effects of Current
Magnets
- Like poles repel, unlike poles attract; a freely suspended magnet rests in the north–south direction. Repulsion is the surest test of a magnet.
- Magnetic field lines go from north to south outside the magnet and south to north inside; they never intersect.
- Magnetic materials: iron, nickel, cobalt. Electromagnets use soft iron; permanent magnets use steel or special alloys (e.g., Alnico).
- The Earth behaves like a huge bar magnet; its geographic north pole is near the Earth’s magnetic south pole. A compass needle is a small magnet.
Magnetic Effect of Current (Oersted, 1820)
- A current-carrying wire produces a magnetic field around it; direction given by the right-hand thumb rule (Maxwell’s corkscrew rule).
- A solenoid (long coil) carrying current behaves like a bar magnet; with a soft-iron core it becomes an electromagnet (used in electric bells, cranes, relays, MRI machines).
- Fleming’s left-hand rule gives the direction of force on a current-carrying conductor in a magnetic field — principle of the electric motor.
- Electromagnetic induction (Michael Faraday, 1831): a changing magnetic field through a coil induces a current. Direction by Fleming’s right-hand rule — principle of the electric generator.
| Device | Principle | Converts |
|---|
| Electric motor | Force on a current-carrying conductor in a magnetic field | Electrical → Mechanical |
| AC / DC generator (dynamo) | Electromagnetic induction | Mechanical → Electrical |
| Transformer | Mutual induction; works only on AC | Steps AC voltage up or down |
| Galvanometer | Torque on a current loop in a magnetic field | Detects current |
AC vs DC
- DC flows in one direction (cells, batteries, solar cells). AC reverses direction periodically (power stations).
- AC is preferred for transmission because its voltage can be changed easily by transformers; power is transmitted at very high voltage to reduce energy loss as heat.
- A step-up transformer increases voltage (at power stations); a step-down transformer decreases it (near homes, in mobile chargers).
13. Atom, Radioactivity, Nuclear Energy & Sources of Energy
Radioactivity
- Spontaneous emission of radiation by unstable nuclei, discovered by Henri Becquerel (1896); Marie and Pierre Curie discovered polonium and radium.
- Alpha (α) particles = helium nuclei (positive charge, least penetrating, stopped by paper).
- Beta (β) particles = fast electrons (negative, stopped by a few mm of aluminium).
- Gamma (γ) rays = electromagnetic waves (no charge, most penetrating, stopped by thick lead or concrete).
- Uses of radioisotopes: Cobalt-60 in cancer treatment, Iodine-131 in thyroid disorders, Carbon-14 in dating fossils and archaeological samples, Uranium-235 as nuclear fuel.
- Units: curie (Ci), becquerel (Bq — SI unit). A Geiger–Müller counter detects radiation.
| Point | Nuclear Fission | Nuclear Fusion |
|---|
| Process | Heavy nucleus (U-235, Pu-239) splits into lighter nuclei when hit by a neutron | Light nuclei (hydrogen isotopes) combine to form a heavier nucleus (helium) |
| Where | Nuclear reactors, atom bomb | Sun and stars, hydrogen bomb |
| Condition | Controlled chain reaction | Extremely high temperature and pressure |
Nuclear Reactor Parts
- Fuel: Uranium-235 / Plutonium-239 (India’s future stages plan to use Thorium).
- Moderator: slows down neutrons — heavy water (D₂O) or graphite.
- Control rods: absorb extra neutrons to control the chain reaction — cadmium or boron.
- Coolant: carries away heat — water, heavy water or liquid sodium.
- Energy comes from conversion of mass into energy — Einstein’s equation E = mc².
| Renewable Sources | Non-renewable Sources |
|---|
| Solar, wind, hydro (water), tidal, geothermal, biomass/biogas, ocean thermal energy | Coal, petroleum, natural gas (fossil fuels), nuclear fuels such as uranium |
Energy One-Liners
- The ultimate source of almost all energy on Earth is the Sun; the Sun’s energy comes from nuclear fusion.
- Solar cells are made mainly of silicon; a solar cooker uses a black box, glass cover and plane mirror reflector.
- Biogas (gobar gas) contains mainly methane (about 75%); the slurry left is good manure.
- A hydroelectric plant converts the potential energy of stored water into electrical energy.