NEET Physics — The Complete Graph Atlas

How to answer any graph question

Graph MCQs look like memory questions. They are not. Every one of them is a formula question in disguise.

The four-question method

Where does it start? At zero, at a finite value, or at infinity? This alone kills most wrong options. (A solid wire's field starts at zero; a hollow pipe's is zero for a while; a thin wire's blows up.)
Is there a kink or a jump? If the question mentions a radius R, a threshold frequency, or a knee voltage, the behaviour must change at that point. A smooth curve through it is wrong.
How fast does it fall or rise? Straight line, 1/x, 1/x², 1/x³, exponential, or sine — six possibilities, and the formula tells you which.
Where does it end? Does it flatten off (saturation, terminal value), keep rising, or come back to zero?

The trick that turns a curve into a straight line. Curves are hard to tell apart by eye; straight lines are not. So if a graph is plotted against the reciprocal and comes out straight, you know the power immediately:

B vs 1/r straight ⇒ B ∝ 1/r ⇒ long straight wire
E vs 1/r² straight ⇒ inverse square ⇒ point charge
r vs √K straight ⇒ r ∝ √K ⇒ charge in a magnetic field

This is also why so many experiment graphs (1/v vs 1/u, for instance) are deliberately plotted that way.

The seven shapes that get confused with each other

Shape	Belongs to	Does NOT belong to
Rise, peak, then 1/r fall	Solid wire; non-conducting charged sphere; g inside/outside Earth	Hollow pipe
Zero, then 1/r fall	Hollow pipe; conducting sphere	Solid wire
Flat and non-zero, then falling	Nothing in the syllabus	— it is always a distractor
Constant inside, then 1/r	Potential of a conducting sphere	Any field graph
Rising exponential	Capacitor charging; LR current growth	Radioactive decay
Falling exponential	Discharge; LR decay; decay law; semiconductor resistivity	Metal resistivity (rises)
Equal-height peaks	Double slit interference	Single slit diffraction (central peak dominates)

Read the axes before anything else. Several standard graphs appear twice in the syllabus with the axes swapped, and the shape flips accordingly. B vs r is a hyperbola; B vs 1/r is a straight line. Resistivity vs T rises for a metal and falls for a semiconductor. Half the marks lost on graph questions come from not checking which variable is on which axis.

Chapters covered

Kinematics — 6 graphs
Laws of motion — 1 graphs
Work, energy, power — 2 graphs
Gravitation — 2 graphs
Mechanical properties — 1 graphs
Thermal properties — 1 graphs
Thermodynamics — 2 graphs
Kinetic theory — 1 graphs
Oscillations — 3 graphs
Electrostatics — 4 graphs
Capacitance — 3 graphs
Current electricity — 4 graphs
Moving charges — 5 graphs
Magnetism — 2 graphs
Electromagnetic induction — 3 graphs
Alternating current — 3 graphs
Ray optics — 3 graphs
Wave optics — 3 graphs
Dual nature — 3 graphs
Nuclei — 2 graphs
Semiconductors — 2 graphs

Kinematics

Uniform velocity

x = x₀ + vt

Straight line. Its slope is the velocity — steeper means faster.

Uniform acceleration

x = ut + ½at²

Parabola opening upward. Curving up means positive acceleration.

Velocity under constant a

v = u + at

Straight line; slope = a, and the area under it = displacement.

Constant acceleration

a = constant

Horizontal line. Area under an a–t graph gives the change in velocity.

Ball thrown upward

v = u − gt

Crosses zero at the top of the flight, then goes negative on the way down.

Projectile path

y = x tanθ − gx²/2u²cos²θ

Parabola. Symmetric about the highest point.

Laws of motion

Friction vs applied force

fₛ ≤ μₛN, fₖ = μₖN

Rises with the applied force, peaks at limiting friction, then drops slightly and stays constant.

Work, energy, power

Spring force

F = −kx

Straight line through the origin. Slope gives the spring constant.

Spring potential energy

U = ½kx²

Parabola with its minimum at the natural length.

Gravitation

g inside and outside the Earth

inside g ∝ r; outside g ∝ 1/r²

Rises linearly to the surface, peaks there, then falls as 1/r².

Gravitational potential energy

U = −GMm/r

Always negative, rising towards zero as r → ∞.

Mechanical properties

Stress–strain curve

Y = stress / strain

Straight (Hooke's law) up to the proportional limit, then yield, ultimate strength, and fracture.

Thermal properties

Anomalous expansion of water

—

Volume is minimum at 4°C, so density is maximum there. Unique to water.

Thermodynamics

Isothermal vs adiabatic

PV = k | PV^γ = k

The adiabatic curve is steeper than the isothermal one through the same point.

Carnot cycle

η = 1 − T₂/T₁

Two isothermals and two adiabatics. Area enclosed = net work done per cycle.

Kinetic theory

Maxwell speed distribution

vₛₛₛ : v̄ : vₕₛₛ = 1 : 1.13 : 1.22

Higher temperature (teal) → peak lower and shifted right. Area under each curve is the same.

Oscillations

Displacement in SHM

x = A sin(ωt + φ)

Sine curve. Velocity leads by 90°, acceleration by 180°.

Acceleration vs displacement

a = −ω²x

Straight line with negative slope through the origin. This shape is the definition of SHM.

KE and PE vs displacement

KE = ½k(A²−x²), PE = ½kx²

Two parabolas that always add to a constant. KE max at the centre, PE max at the ends.

Electrostatics

Field of a point charge

E = kq/r²

Pure inverse-square decay. Compare with 1/r for a wire and 1/r³ for a dipole.

Charged CONDUCTING sphere

inside E = 0; outside E = kq/r²

Zero inside, jumps at the surface, then 1/r². All the charge sits on the surface.

Uniformly charged NON-conducting sphere

inside E ∝ r; outside E ∝ 1/r²

Rises linearly inside, peaks at the surface, then 1/r². Same shape as a thick current-carrying wire.

Potential of a conducting sphere

inside V = kq/R; outside V = kq/r

Constant inside (not zero!), then falls as 1/r. Field is zero inside but potential is not.

Capacitance

Charge vs voltage

Q = CV

Straight line through the origin; slope = C. Area under it = energy stored.

Charging a capacitor

Q = Q₀(1 − e^−t/RC)

Rising exponential, flattening at Q₀. Reaches 63% in one time constant.

Discharging a capacitor

Q = Q₀e^−t/RC

Falling exponential. Drops to 37% of its value in one time constant.

Current electricity

Ohmic conductor

V = IR

Straight line through the origin. Slope = 1/R, so a steeper line means lower resistance.

Resistivity of a metal

ρ = ρ₀[1 + α(T − T₀)]

Increases with temperature for metals.

Resistivity of a semiconductor

ρ ∝ e^Eₕ/2kT

Decreases with temperature — the opposite of a metal. Common comparison question.

Terminal voltage of a cell

V = ε − Ir

Falling straight line. Intercept = emf, magnitude of slope = internal resistance.

Moving charges

Solid current-carrying wire

inside μ₀Ir/2πa²; outside μ₀I/2πr

Linear rise from zero, peak at the surface, then 1/r fall. The most-repeated graph in the chapter.

Hollow current-carrying pipe

inside B = 0; outside μ₀I/2πr

Zero inside — no current is enclosed. Jump at the surface, then 1/r.

Long thin wire

B = μ₀I/2πr

Pure 1/r hyperbola — no inside region, so no kink.

Radius vs speed

r = mv/qB

Straight line through the origin.

Time period vs speed

T = 2πm/qB

Horizontal line — there is no v in the formula. Heavily tested.

Magnetism

Hysteresis loop

—

Retentivity is the B-intercept, coercivity the H-intercept. Loop area = energy lost per cycle.

Susceptibility vs temperature

Curie law: χ = C/T

Paramagnetic (maroon) falls as 1/T; diamagnetic (teal) is small, negative and independent of T.

Electromagnetic induction

Current growth in an LR circuit

I = I₀(1 − e^−Rt/L)

Rising exponential; reaches 63% of the final value in one time constant L/R.

Current decay in an LR circuit

I = I₀e^−Rt/L

Falling exponential. Never quite reaches zero.

Emf of a rotating coil

ε = NABω sinωt

Sine curve — this is where alternating current comes from.

Alternating current

Reactance vs frequency

X₃ = 1/2πfC | X₄ = 2πfL

Capacitive reactance (maroon) falls as 1/f; inductive reactance (teal) rises linearly.

Resonance curve

f₀ = 1/2π√(LC)

Peak at resonance, where X₄ = X₃. Lower resistance (maroon) gives a sharper peak — higher Q factor.

Impedance vs frequency

Z = √(R² + (X₄−X₃)²)

Minimum at resonance, where Z = R. Mirror image of the current curve.

Ray optics

1/v vs 1/u for a lens

1/v − 1/u = 1/f

Straight line. Both intercepts give 1/f — a standard experiment graph.

Deviation in a prism

μ = sin[(A+δₘ)/2] / sin(A/2)

Dips to a minimum deviation and rises again. At that point the ray passes symmetrically.

Refractive index vs wavelength

Cauchy: μ = A + B/λ²

Violet bends most, red least. This is why a prism disperses white light.

Wave optics

Young's double slit intensity

I = 4I₀cos²(φ/2)

All maxima are the same height and evenly spaced — this is what distinguishes interference from diffraction.

Single slit diffraction

a sinθ = nλ

A broad bright central maximum with much fainter side maxima. The central peak is twice as wide.

Malus's law

I = I₀cos²θ

Falls from I₀ at 0° to zero at 90°.

Dual nature

Stopping potential vs frequency

eV₀ = hν − φ₀

Straight line with slope h/e, cutting the axis at the threshold frequency. Slope is the same for every metal.

Photocurrent vs intensity

—

Straight line through the origin. Intensity controls the number of electrons, not their energy.

Photocurrent vs collector voltage

—

Same stopping potential, different saturation currents ⇒ same frequency, different intensities.

Nuclei

Binding energy per nucleon

—

Peaks near A ≈ 56 (iron). Light nuclei fuse and heavy nuclei fission because both move towards the peak.

Radioactive decay

N = N₀e^−λt

Exponential decay. Halves every half-life, and never reaches zero.

Semiconductors

p–n junction characteristic

—

Almost nothing until the knee voltage (0.7 V for Si, 0.3 V for Ge), then a steep rise. Tiny reverse current.

Zener diode

—

Used in reverse breakdown, where the voltage stays fixed while the current changes — hence voltage regulation.

Using this atlas

Cover the picture, read the formula, draw the graph. Then compare. This is the only practice that transfers to the exam — recognising a shape from four options is a weaker skill than producing it, and it collapses under time pressure.
Work chapter by chapter, in step with whatever is being taught. Do not try to absorb all 56 at once.
Pay special attention to the pairs that differ by one word: solid vs hollow, metal vs semiconductor, interference vs diffraction, isothermal vs adiabatic. NEET builds distractors out of exactly these.
For every graph, be able to say what the slope means and what the area means. Slope of v–t is acceleration; area under it is displacement. Slope of Q–V is capacitance; area is energy. Examiners ask about slopes and areas far more often than about shapes alone.

The three graphs most worth over-learning

Solid conductor B vs r — asked in five separate NEET papers, and one of the two graph questions missed on the 9 August ILTS.
Stopping potential vs frequency — the slope is h/e and is the same for every metal; only the intercept changes.
Binding energy per nucleon vs A — the peak near iron explains both fusion and fission in one picture.