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.
300 fundamentals
“When a gas expands in a piston, the piston lifts, showing the gas does work on its surroundings.”
The first law states ΔU = Q – W, where W is work done by the system. Heat added (+Q) raises internal energy, while work done by the gas (positive W) reduces it. The usual mistake is to add W for expansion instead of subtracting.
Memory trick: ΔU = Q – W (Q in, W out)
“Stacking two water tanks side by side doubles the stored volume (parallel C), but linking them end-to-end shares the same level, so 1/C adds (series).”
For capacitors in parallel the voltage across each is the same, so total capacitance Cₚ = ΣC. In series the charge on each is identical, giving 1/Cₛ = Σ1/C. Trap: swapping the formulas with resistors or forgetting voltage equality in parallel.
Memory trick: Parallel C adds; Series 1/C adds – opposite of resistors.
“A sliding ruler that measures voltage without pulling any current, like a bathroom scale reads weight without adding weight.”
In a potentiometer the unknown emf is compared with a known potential drop along a uniform wire; at the null point no current is drawn, giving the true emf. It measures voltage without internal resistance loading. Trap: forgetting the null condition; any current invalidates the reading.
Memory trick: Null → true EMF, no draw
“A compass needle (ferromagnetic) snaps to Earth’s field, water (diamagnetic) barely lifts in a strong magnet, and liquid oxygen (paramagnetic) is drawn toward it.”
Ferromagnets have permanent dipoles that align, giving strong attraction; paramagnets have unpaired electrons that align only in an external field, giving weak attraction; diamagnets induce opposite dipoles, causing weak repulsion. Remember that some alloys (e.g., certain stainless steels) may look non-magnetic but are not true diamagnets.
Memory trick: D-P-F: Dull repels, Pushes weakly, Forces strongly.
“When you look at yourself in a makeup mirror, the size change follows m = –v/u.”
Magnification m = image height/object height = –v/u for mirrors; the minus sign gives an inverted real image, while a positive m indicates an upright virtual image. The common mistake is dropping the sign or using +v/u, which gives wrong orientation.
Memory trick: m = –v/u (mirror), m = v/u (lens)
“A diode is a one-way street: forward bias opens the lane for cars (electrons), reverse bias puts up a roadblock.”
A p-n junction allows large current when forward biased (V>0) and blocks it when reverse biased (V<0). Built-in potential ≈0.7 V for Si. Trap: reverse leakage isn’t zero; Zener breakdown appears at high reverse voltage.
Memory trick: Forward low R, Reverse high R
“When you scroll from FM radio to X-ray images on a medical screen, each step jumps to a higher frequency band.”
The electromagnetic spectrum ordered by increasing frequency is: radio → microwave → infrared → visible → ultraviolet → X-ray → gamma. Higher frequency means shorter wavelength (λ = c/ν) and larger photon energy (E = hν). Students often reverse the order by mixing up wavelength with frequency.
Memory trick: R-M-I-V-U-X-G = Rise in frequency
“When a stone tied to a string whirls overhead, the string pulls the stone inward, showing the centripetal acceleration.”
In uniform circular motion the speed is constant but the velocity direction continuously changes, giving an acceleration a = v²/r directed toward the centre. The inward centripetal force (tension, gravity, friction) supplies this acceleration via F = ma. Exam trap: forgetting the vector nature leads to writing acceleration outward or omitting the direction.
Memory trick: Centripetal = ‘Center Pull’, think of a string pulling inward.
“Sunlight warming your face on a clear day is pure radiation, not moving air.”
Radiation travels through vacuum as EM waves, while conduction needs direct contact and convection needs a moving fluid. The common mistake is to describe solar heating as convection; in reality the Sun’s energy reaches Earth only by radiation. Remember to choose the correct mode when no medium exists.
Memory trick: Space = No air → No convection.
“When you heat water, each moving molecule’s kinetic energy rises by ½kT per active quadratic mode.”
Equipartition says each active quadratic DoF contributes (1/2)k_B T per molecule to internal energy. Thus U = f nRT/2, C_V = fR/2 and γ = (f+2)/f for an ideal gas, where f is the total number of active DoF. Only modes that are not frozen count.
Memory trick: U = f·RT/2 → C_V = f·R/2
“Sliding a glass slab into a capacitor is like slipping a sponge into a bowl; the bowl now holds more water for the same pressure.”
A dielectric polarises in the field, creating an opposing field that reduces the net field. For an isolated capacitor Q stays constant, so the voltage drops and the capacitance C = Q/V increases by the dielectric constant K. First decide what is fixed (Q or V).
Memory trick: Isolated: Q const → V↓, C↑ (×K).
“A playground swing reaches its highest point after the push stops, just as B lags behind H in a ferromagnet, forming a loop.”
In a ferromagnet the magnetisation B does not follow the applied field H instantly; the lag creates a hysteresis loop on the B-H graph. The loop’s enclosed area equals the energy dissipated per unit volume each cycle. Exam nuance: coercivity is the field to reduce B to zero, remanence is the residual B; mixing them gives wrong answers.
Memory trick: Loop area = loss; wide = hard magnet.
“The bright yellow glow of a sodium street lamp comes from electrons jumping between bound levels, not from the atoms being ripped apart.”
Excitation moves an electron to a higher bound orbit, so the total energy stays negative (E = –13.6 eV/n²). Ionisation supplies at least the ionisation energy, raising the electron to n = ∞ where the energy becomes zero; any extra energy appears as kinetic energy of the free electron. The trap: assuming any photon above visible light ionises – only photons with E ≥ 13.6 eV (for H) cause ionisation.
Memory trick: Excite = stay negative; Ionise = reach zero.
“A 1 kBq source feels harmless, but it can still give a high dose if held close, because Bq measures decays, not energy.”
Activity counts how many decays occur per second; it says nothing about the energy released or how much is absorbed by tissue. Dose depends on decay energy, radiation type and shielding. The mistake is treating Bq as a dose unit.
Memory trick: Bq = decays / sec, not joules / sec.
“When a Wheatstone bridge balances, the galvanometer is silent, just like a perfectly tuned guitar string produces no buzz.”
At balance the galvanometer carries no current, so the bridge is in equilibrium. The unknown resistance R₁ and known resistance R₂ satisfy R₁/R₂ = l₁/l₂, where l₁ and l₂ are the lengths of the two wire segments. This holds only for a uniform wire and negligible end effects. Forgetting the zero-galvanometer condition gives a wrong ratio.
Memory trick: Zero galvanometer → R₁/R₂ = l₁/l₂.
“A stone dropped in a pond creates ripples; their speed equals how fast the crests pass (frequency) times the distance between crests (wavelength).”
For any wave traveling in a uniform medium, v = f·λ, where f and λ belong to the same wave. It cannot mix the frequency of one wave with the wavelength of another, nor change medium. The exam trap is using f of sound with λ of light, which is invalid.
v = f lambda
Memory trick: v = f×λ – same wave, same medium
“A rectangular coil in a uniform magnetic field acts like a tiny electric motor, feeling a twist but no push.”
In a uniform B, forces on opposite sides of a current loop are equal and opposite, giving zero net force but a couple that produces torque τ = m × B, where m = N I A (area vector). The key nuance: zero net force does not imply zero rotational effect. The exam trap is forgetting torque when net force cancels.
Memory trick: Zero net force ≠ zero torque; think of a seesaw
“Two speakers playing the same note in sync sound louder (constructive); out of sync you hear a dip (destructive).”
Constructive interference occurs when the path difference is an integer multiple of the wavelength (Δ = nλ), making waves in phase and intensity maximum. Destructive interference occurs for a half-integer multiple (Δ = (n+½)λ), giving opposite phases and intensity minimum. Mistaking (n+½)λ for bright is a frequent error.
Memory trick: nλ bright, (n+½)λ dark
“Your phone charger steps 230 V down to 5 V, whereas a microwave transformer steps the same mains up to thousands of volts.”
In a transformer V_s/V_p = N_s/N_p and I_s/I_p = N_p/N_s, so more secondary turns raise voltage (step-up) and lower current, fewer turns do the opposite (step-down). Power ≈ constant (neglecting losses). Trap: forgetting the inverse current ratio when applying the turns ratio.
Memory trick: More turns → higher V, lower I; fewer turns → lower V, higher I
“Reading 36.7 °C on a digital thermometer shows three significant figures – the ‘7’ is the last reliable digit.”
Significant figures are the digits known with certainty plus the first uncertain digit, reflecting the instrument’s precision. In multiplication or division the final answer must retain the same number of significant figures as the factor with the fewest. A frequent trap is to keep extra digits from intermediate steps or to count leading zeros as significant.
Memory trick: Multiply/divide → keep the least SF
“A car’s speedometer reads the tangent slope of its position-time graph at that exact moment.”
Instantaneous velocity is the derivative ds/dt, the slope of the s-t curve at a single point. It differs from average velocity which uses a finite interval. In graphs, draw the tangent line to get the value.
Memory trick: Instant v = slope of s-t at a point
“A spinning carnival ride’s hanging light shows a conical pendulum, where the string’s tilt supplies the circular pull.”
A mass m on a string of length L makes an angle θ with the vertical and moves in a horizontal circle of radius r = L sinθ. The horizontal component of the tension supplies the centripetal force: T sinθ = mv²/r. The common slip: forgetting that tension, not weight, gives the inward pull.
Memory trick: Tension’s horizontal part = mv²/r.
“Pushing a shopping cart forward while it rolls straight illustrates work done by the applied force.”
Work is the scalar product of force and displacement: W = F·d·cosθ, where θ is the angle between them. Only the component of force along the motion contributes to energy transfer. Common error: omitting the cosine factor for angled forces.
Memory trick: W = F·d·cosθ – only parallel part counts
“A child on a rotating stool spins faster when pulling a book toward the centre.”
When a skater pulls her arms inward, I decreases and ω increases so that L = I ω remains constant. The mistake is to think the internal motion creates extra torque; internal forces cannot change total L. Forgetting this gives incorrect ω values.
Memory trick: Pull in → I↓, ω↑ (L unchanged)