Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“Sweating cools you because evaporating water carries away latent heat.”
Heat absorbed or released during a change of state, at constant temperature.
Q = mL
Memory trick: Phase change hides the heat.
“Camera flashes dump a capacitor's stored charge in a bright instant.”
A capacitor stores charge per volt; parallel-plate C = ε₀A/d.
C = ε₀A/d
Memory trick: Bigger plates, closer together → more storage.
“They're just conservation of charge and energy dressed up for circuits.”
Junction rule: charge is conserved (currents in = out). Loop rule: energy is conserved (voltage gains = drops).
Memory trick: Junction = charge; loop = energy.
“Power lines ship electricity at high voltage, then transformers step it down for your home.”
Transformers change AC voltage using the ratio of coil turns; they don't work on DC.
Vₛ/Vₚ = Nₛ/Nₚ
Memory trick: Turns ratio sets voltage ratio.
“Your eye's lens changes shape to keep u, v and f in balance so images land on the retina.”
For a thin lens, 1/v − 1/u = 1/f.
1/v − 1/u = 1/f
Memory trick: Mind the sign convention.
“Electron microscopes exploit the electron's tiny wavelength to see viruses.”
Every particle has a wavelength λ = h/p, noticeable only for tiny masses.
λ = h/p
Memory trick: Matter waves matter only at atomic scale.
A frequent error is saying electromagnetic waves require a material medium. In reality, A changing electric field produces magnetic effects and a changing magnetic field produces an electric field. This coupled disturbance can travel through vacuum without charges continuously carrying it forward.
Memory trick: changing E makes B; changing B makes E.
A frequent error is using the resultant speed as the horizontal speed throughout the flight. In reality, Gravity changes only the vertical velocity of a projectile. Horizontally, velocity stays constant when air resistance is ignored. The two motions share the same clock but otherwise evolve independently.
Memory trick: one clock, two equations: solve x and y separately, then recombine.
In an insulated mixture, energy lost by hotter bodies equals energy gained by colder bodies until they reach a common temperature. Use signed heat changes or a clear lost = gained equation, never both conventions at once.
Memory trick: the larger heat capacity pulls the final temperature closer to itself.
A frequent error is saying every molecule has the same speed at a given temperature. In reality, For an ideal gas, absolute temperature measures average translational kinetic energy per molecule: 3k_BT/2. At the same temperature, light and heavy molecules have the same average translational energy but different rms speeds.
Memory trick: same average energy, lighter molecules move faster.
A frequent error is assuming electric field points toward higher potential. In reality, The electric field points in the direction in which potential decreases most rapidly. Along one dimension E_x = -dV/dx; the minus sign carries the direction information.
Memory trick: a positive test charge naturally moves downhill in potential.
A frequent error is expecting a cut magnet to leave one north-only and one south-only piece. In reality, Cutting a bar magnet produces smaller north-south dipoles, not separate monopoles. Therefore net magnetic flux through any closed surface is zero.
Memory trick: every cut makes two complete magnets.
A frequent error is imagining an electron radiating continuously while remaining in an allowed orbit. In reality, Bohr allowed only orbits with angular momentum n h/(2pi). An electron in a stationary orbit does not radiate; light is emitted or absorbed only during a transition.
Memory trick: no light within an orbit; photon only during a jump.
A frequent error is subtracting masses in the wrong direction and obtaining negative binding energy. In reality, A bound nucleus has less mass than its separated nucleons. The missing mass corresponds to the energy released during binding: B = Delta m c^2.
Memory trick: separated nucleons minus nucleus gives positive mass defect.
A frequent error is calling tightly clustered but shifted readings accurate. In reality, Accuracy means closeness to the accepted value; precision means repeatability. Repeated measurements can reduce random uncertainty but cannot remove a systematic calibration error.
Memory trick: tight cluster is precise; correct centre is accurate.
A frequent error is adding intensities directly before considering phase. In reality, When waves overlap, their displacements add algebraically at each point. Constructive and destructive interference are consequences of this linear addition, not permanent destruction of energy.
Memory trick: add displacements with phase first, then find intensity.
A frequent error is using the total speed to find the circular radius when motion is helical. In reality, A velocity component perpendicular to B produces circular motion, while a parallel component remains unchanged. Together they make a helix whose pitch depends on the parallel speed.
Memory trick: v_perp sets radius; v_parallel sets pitch.
A frequent error is mixing up the conditions for bright and dark fringes. In reality, bright fringes form where the path difference is a whole number of wavelengths, dark where it's an odd number of half-wavelengths.
Memory trick: path diff = nλ → bright; (n+½)λ → dark.
A frequent error is taking the 220 V mains as the peak voltage. In reality, the effective (root-mean-square) value of AC that delivers the same heating as a steady DC; Vrms = V0/√2.
Memory trick: 220 V mains is the rms value; the peak is about 311 V.
A frequent error is thinking the depletion region has free charge carriers. In reality, the charge-free zone at a p–n junction that sets up a built-in barrier potential.
Memory trick: it's 'depleted' of carriers — that's what creates the barrier.
“It measures a coin's thickness far better than any ruler.”
A vernier scale lets you read lengths to 0.1 mm by aligning scale marks.
Memory trick: Read main + vernier coincidence.
“When the clock isn't given, this is your go-to equation.”
v² = u² + 2as links velocity and displacement without time.
v² = u² + 2as
Memory trick: No 't'? Use v² = u² + 2as.
“A gun recoils backward exactly to balance the forward momentum of the bullet.”
With no external force, total momentum of a system stays constant.
Memory trick: No external force → total p is fixed.
“A pendulum trades height for speed and back, forever (without friction).”
Energy can't be created or destroyed, only transformed; total energy stays constant.
Memory trick: Energy changes form, never vanishes.