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
“Ice cubes melt in your drink without the temperature rising until all ice disappears.”
Latent heat L is the energy absorbed or released during a phase change at constant temperature; Q = mL. The temperature stays unchanged until the entire mass changes phase, a point often missed in multi-step questions.
Q = mL
Memory trick: Phase change = heat, no ΔT.
“Two parallel plates of a sandwich act like a capacitor: larger area or smaller gap (A/d) stores more charge.”
Capacitance C = ε₀A/d measures charge stored per volt. Increasing plate area A raises C; increasing separation d lowers C. The trap: forgetting ε₀ for a vacuum capacitor or mixing up series and parallel formulas—always keep C ∝ A/d.
C = ε₀A/d
Memory trick: C up with A, down with d.
“Water entering a junction equals water leaving; around a loop the pump’s rise equals the drops.”
Junction (Kirchhoff’s current) rule: ΣI_in = ΣI_out, i.e., algebraic sum of currents at a node is zero. Loop (Kirchhoff’s voltage) rule: ΣV around any closed loop is zero, accounting for rises and drops. Trap: mixing up sign conventions for rises vs drops.
Memory trick: Node: ΣI=0; Loop: ΣV=0
“Plugging a phone charger into a wall socket, the tiny transformer steps 230 V down to 5 V for the phone.”
For an ideal transformer Vₛ/Vₚ = Nₛ/Nₚ and Iₛ/Iₚ = Nₚ/Nₛ; it works only with alternating current because a changing flux is needed. A common trap is to think voltage alone is conserved – actually power (V·I) is (ignoring losses).
Vₛ/Vₚ = Nₛ/Nₚ
Memory trick: Turns ratio = voltage ratio – more turns, higher voltage
“A camera lens forms a sharp image on film when 1/v − 1/u = 1/f, just like adjusting focus on a smartphone.”
For a thin lens, 1/v − 1/u = 1/f with sign convention: object distance u is negative (real object), image distance v positive for real image on opposite side, f positive for convex, negative for concave. The common mistake is forgetting the minus sign before 1/u, leading to wrong magnitudes.
1/v − 1/u = 1/f
Memory trick: 1/f = 1/v – 1/u; u taken negative.
“An electron in an electron microscope shows diffraction like light, because its λ = h/p is comparable to atomic spacings.”
A particle’s wavelength λ = h/p; for electrons p is small enough that λ matches atomic distances, producing diffraction. For macroscopic objects λ is ≪ observable. Trap: using mass instead of momentum in λ = h/p.
λ = h/p
Memory trick: λ = h/p; tiny unless p tiny.
“Even in the vacuum of space, sunlight reaches Earth, proving EM waves need no air or water.”
A common misconception is that EM waves require a material medium. In reality the self-sustaining E-B coupling allows propagation in vacuum. The mistake often appears when students draw the wave inside a rope—remember, no medium is needed.
Memory trick: Vacuum = no medium needed
“A stone dropped from a moving bus keeps the bus’s forward speed while it falls to the ground.”
In projectile motion without air resistance the horizontal velocity stays constant; gravity only changes the vertical component. Both components share the same time, so use x = uₓt and y = uᵧt – ½gt² separately and then combine. The common error is to assume the resultant speed equals the horizontal speed for the whole flight.
Memory trick: Horizontal = constant; Vertical = g-affected; same t → solve separately
“When hot coffee is poured into a cold mug, the coffee cools and the mug warms until they share a single temperature.”
In an isolated system the algebraic sum of all heat exchanges is zero: ΣQ = 0. Write each term as Q = mcΔT for sensible changes or Q = mL for phase changes, using the same sign convention (+ for heat absorbed, – for heat released). A frequent error is to write “heat lost = heat gained” and also assign opposite signs, which double-counts the heat and gives a wrong final temperature.
Memory trick: One sign rule: + for heat absorbed, – for heat released; then ΣQ=0.
“When you feel a hot pan, the sizzling oil’s molecules share the same average energy, yet the lighter steam molecules zip away faster.”
Absolute temperature T is defined by the average translational kinetic energy of a molecule: ⟨KE⟩ = 3k_B T/2. Thus at a given T all ideal gases have identical ⟨KE⟩, but rms speed v_rms = √(3k_B T/m) so lighter molecules move faster. The common trap is assuming every molecule has the same speed; the Maxwell-Boltzmann distribution gives a spread of speeds.
Memory trick: Same T → same 3/2 kT energy; v_rms ∝ 1/√m
“A skier always slides down the slope, never up; likewise E points down potential.”
A common error is to think the electric field points toward higher potential. Actually, E points toward decreasing V, expressed as E = -∇V. Missing the minus sign flips the direction and gives a wrong answer.
Memory trick: Minus sign = downhill direction
“A student expects a sliced magnet to give a north-only half like a peeled orange, but each half still holds both poles.”
Cutting a magnet never produces a lone north or south pole; each piece retains both poles, forming two dipoles. Forgetting this leads to the mistaken belief of magnetic monopoles and wrong flux or field-line counts in problems.
Memory trick: Every cut keeps N-S together.
“A car cruising at constant speed is silent; it only roars when it accelerates.”
In Bohr’s model an electron in an allowed orbit does not emit radiation; photons appear only during transitions between quantised levels. The trap is mixing classical radiation (continuous loss) with quantum stationary states.
Memory trick: No sound = no light in steady orbit.
“Subtracting the nucleus mass from the nucleons the wrong way gives a ‘negative binding energy’ – like paying back more than you borrowed.”
Error: using M_nucleus – Σm_individual yields negative Δm. Correct order (nucleons minus nucleus) gives positive Δm and a positive binding energy, the energy released on formation.
Memory trick: Nucleons – nucleus = positive Δm
“A GPS that shows a tight cluster of points off the road is precise but not accurate.”
Calling a tightly clustered set of readings accurate ignores systematic shift. Only when the cluster centre coincides with the true value is the measurement accurate; otherwise it is merely precise.
Memory trick: Cluster ≠ correct centre.
“Two laser beams crossing don’t become brighter just because both are on; their fields must add before intensity is computed.”
A common error is I_total = I₁ + I₂ regardless of phase. Correctly, add the electric fields (or amplitudes) with sign, then compute intensity ∝ (E₁+E₂)². Ignoring phase gives wrong fringe contrast.
Memory trick: Fields add, intensity follows.
“A screw driven straight into wood still rotates around its axis; the rotation radius depends on the sideways push, not the total push.”
For helical motion the circular radius is set solely by the perpendicular speed v⊥: r = mv⊥/(|q|B). The parallel speed only stretches the helix (pitch). Using the total speed overestimates r, a common error.
Memory trick: Only sideways speed decides circle size.
“When you see a dark band at the centre of a Young’s pattern, it signals a half-wavelength extra path, not a full wavelength.”
Students often reverse bright and dark conditions. The centre is bright only if the two waves arrive in phase (Δ = 0, nλ). If a half-wave shift (Δ = λ/2) occurs, the centre becomes dark. Remember the ‘whole λ = bright, half λ = dark’ rule.
Memory trick: Whole λ → bright; half λ → dark.
“If you plug a 220 V lamp into a 311 V source, it would burn out—showing 220 V is rms, not peak.”
A frequent mistake is reading the mains rating as the peak voltage. The 220 V specification is the rms value; the actual instantaneous peak is V0 = √2·Vrms ≈ 311 V. Problems ask for peak or rms, so convert correctly.
Memory trick: Peak = √2 × rms; rms = Peak ÷ √2.
“Like the quiet zone in a battery where ions sit but electrons can’t flow, the p-n depletion region has only ionized atoms, no free carriers.”
The depletion region of a p-n junction contains no mobile electrons or holes; it is filled with fixed ionized donor (positive) and acceptor (negative) atoms. These space-charge ions produce the internal electric field and the built-in barrier potential. A common trap is treating the region as electrically neutral, which gives wrong barrier values.
Memory trick: Depletion = no mobile carriers, only fixed ions.
“When you slide a Vernier caliper over a screw, each time a vernier mark lines up with a main-scale mark you read an extra 0.1 mm.”
A Vernier caliper gives a reading = main-scale reading + (number of coinciding vernier divisions × least-count, usually 0.1 mm). Zero error is the reading when the jaws are closed; if it is positive, subtract it, if negative, add it. Students often forget to apply the sign of zero error, leading to a wrong final value.
Memory trick: Main + (Vernier×0.1 mm) – zero error
“A skier sliding down a hill reaches 20 m/s after descending 30 m, satisfying v² = u² + 2as.”
For constant acceleration, the square of the final speed equals the square of the initial speed plus twice the product of acceleration and displacement. It eliminates time, handy when time isn’t given. Ensure the sign of a matches the direction of s.
v² = u² + 2as
Memory trick: V² = U² + 2·A·S
“Two ice skaters push off each other and glide apart with opposite speeds.”
If no external force acts, the vector sum of all momenta in a system remains constant before and after an interaction. This follows from Newton’s third law. Include every object; missing a piece breaks the conservation check.
Memory trick: Σp_i = Σp_f if no external force.
“A swinging pendulum trades its height for speed; the sum of kinetic and potential energy stays constant.”
In an isolated system, total mechanical energy (KE + PE) remains constant; energy only changes form. If friction or air resistance act, mechanical energy is not conserved. Trap: assuming conservation when non-conservative forces are present.
Memory trick: Etotal constant if no loss