Experimental Skills Formula Sheet — JEE Main Physics

Q: What are the most important Experimental Skills formulas for JEE Main?

This Experimental Skills formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Vernier calipers usage, Screw gauge usage, Simple pendulum experiments, Metre scale - principle of moments, Young's modulus determination — each shown with the key result and, where useful, a worked example.

Q: Is this Experimental Skills formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

Q: How should I revise Experimental Skills formulas?

Blurt the Experimental Skills formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Every key Experimental Skills formula, definition and theorem for JEE Main Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 18 sub-topics

Vernier calipers usage
Screw gauge usage
Simple pendulum experiments
Metre scale - principle of moments
Young's modulus determination
Surface tension by capillary rise
Coefficient of viscosity
Speed of sound using resonance tube
Specific heat capacity determination
Resistivity measurement using metre bridge
Resistance using Ohm's law
Galvanometer figure of merit
Focal length determination
Angle of deviation vs angle of incidence plot
Refractive index of glass slab
p-n junction diode characteristics
Zener diode characteristics
Component identification

Errors & Measurement Fundamentals

Accuracy vs precision:

Accuracy

=

closeness to the true value (low systematic error).

Precision

=

closeness of repeats (low random error).

Least count

=

smallest division an instrument reads.

Types of error

▸ $Systematic$ (one-sided): instrumental/zero/personal — correctable.
▸ $Random$ (both signs): cut by repeating & averaging.
▸ $Least-count error$ : the resolution limit.

Mean & relative error

\overline{a} = \frac{\sum a _{i}}{n}, Δ \overline{a} = \frac{\sum ∣Δ a _{i} ∣}{n}, δ a = \frac{Δ a}{a}

Δ \overline{a} =

mean absolute error

Propagation of error

z = a \pm b : Δ z = Δ a + Δ b; z = \frac{a ^{p} b ^{q}}{c ^{r}} : \frac{Δ z}{z} = p \frac{Δ a}{a} + q \frac{Δ b}{b} + r \frac{Δ c}{c}

errors ALWAYS add (worst case)

Four dartboards illustrating the combinations of accuracy and precision — Accuracy $=$ on target; precision $=$ tightly grouped.

Significant figures

▸Non-zero digits & zeros between them count; leading zeros don't.
▸ $\times$ / $\div$ : keep the fewest s.f.; $+$ / $-$ : keep the fewest decimal places.

🚫 Examiner Trap · Errors & measurement

(1) Errors

always add

— even for

a - b

(and the % error then blows up for small

a - b

). (2) Multiply each fractional error by its

power

(

2 \times

for

r^{2}

\frac{1}{2}

for

). (3) Max error in one reading

=

least count. For N oscillations:

Δ T / T =

LC/(total time). (4) Changing units doesn't change s.f. count.

Vernier, Screw Gauge & Metre Scale

Comparative: vernier vs screw gauge

	Vernier	Screw gauge
Least count	$0.1$ mm	$0.01$ mm
LC formula	$1 MS D - 1$ VSD $= \frac{MSD}{N}$	$\frac{pitch}{CSD}$
Reading	MSR $+ V S D \times$ LC	MSR $+ CS D \times$ LC

Vernier / Screw gauge

LC_{V} = 1 MSD - 1 VSD; LC_{S} = \frac{pitch}{CSD}

pitch

=

distance moved per full rotation;

N

VSD coincide with

(N - 1)

MSD

Vernier zero-error: positive (vernier zero to the right of main-scale zero, subtract) and negative (vernier zero to the left, add) — Zero error: $+ \to$ subtract, $- \to$ add.

Screw-gauge zero error: circular-scale zero below the reference line (positive, subtract) versus above it (negative, add) — Correct for zero error and backlash.

Metre scale — moments

m_{1} d_{1} = m_{2} d_{2}

balance a metre rule on a knife-edge; find unknown mass from balancing distances

🚫 Examiner Trap · Instruments & zero error

(1) Correction is

always subtract the signed zero error

— so a

negative

zero error is ADDED. (2) Turn the screw

one way only

near the reading to avoid backlash. (3) Pitch

=

dist

/

rotations — not one division. (4) For

-

ve vernier error:

- (N - coinciding) \times

LC.

Mechanics Experiments

Simple pendulum — g

T = 2 π \frac{L}{g} \Rightarrow g = \frac{4 π ^{2} L}{T ^{2}}

effective length

L =

thread

+

hook

+

bob radius

Simple pendulum and an L versus T-squared straight-line graph whose slope equals g over 4 pi squared — Plot L vs $T^{2}$ : slope $= g /4 π^{2}$ .

Pendulum tips

▸Small amplitude ( $< 1 0^{\circ}$ ) keeps it SHM.
▸Time $\sim 20$ oscillations to cut timing error; $T = t / n$ .

Young's modulus (Searle)

Y = \frac{M gL}{π r ^{2} ℓ}

ℓ =

extension under load Mg,

L =

length,

r =

wire radius (measured with a screw gauge)

Searle's double-wire apparatus (reference wire Q and experimental wire P with micrometer) and an extension-versus-load straight line — Plot $ℓ$ vs W: $Y = \frac{M gL}{π r ^{2} ℓ}$ .

🚫 Examiner Trap · Mechanics experiments

(1) Pendulum: T error is doubled in g (since

g \propto 1/ T^{2}

) — time MANY oscillations; add HALF the bob diameter to length. (2) Plot L vs

T^{2}

(a straight line), NOT L vs T. (3) Searle's r enters as

r^{2}

— its small error doubles; the

two-wire

design cancels temperature & support yielding.

Fluids, Heat & Sound

Surface tension (capillary)

h = \frac{2 S cos θ}{ρ g r} \Rightarrow S = \frac{h ρ g r}{2 cos θ}

r =

tube radius,

θ =

contact angle; detergent lowers S

Viscosity (terminal velocity)

η = \frac{2 r ^{2} ( ρ - σ ) g}{9 v}; F_{v i sc} = 6 π ηr v

ρ =

sphere density,

σ =

liquid density,

v =

terminal velocity

Specific heat (mixtures)

m_{s} c_{s} (T_{s} - T) = m_{w} c_{w} (T - T_{w})

heat lost by solid

=

heat gained by water

+

calorimeter

Speed of sound (resonance tube)

v = 2 f (l_{2} - l_{1}); e = \frac{l _{2} - 3 l _{1}}{2}

l_{1}, l_{2} =

first two resonance lengths,

e =

end correction

Resonance tube partly filled with water, a tuning fork at the mouth, and the first two resonance column lengths l1 and l2 — $v = 2 f (l_{2} - l_{1})$ removes the end correction.

🚫 Examiner Trap · Fluids, heat & sound

(1) Viscosity uses

(ρ - σ)

— subtract the liquid's density (buoyancy); if

ρ < σ

the body rises. (2) Resonance:

λ = 2 (l_{2} - l_{1})

cancels

the end correction — using

4 l_{1}

alone does not. (3) Calorimetry: include the calorimeter's water-equivalent in 'heat gained'. (4) Capillary rise

h \propto 1/ r

— a narrower tube lifts higher.

Electricity Experiments

Metre bridge

\frac{R}{S} = \frac{l}{100 - l} \Rightarrow S = R \frac{100 - l}{l}; ρ = \frac{S π r ^{2}}{L} = \frac{S π d ^{2}}{4 L}

balance

=

no galvanometer deflection;

l =

balancing length (cm)

Metre bridge: known resistance R and unknown S in the top arm, a 1 metre wire AC with a sliding jockey, and a galvanometer that reads zero at the balance length l — Balance length l gives S, then $ρ$ .

Ohm's law

R = \frac{V}{I} (slope of V - I)

Galvanometer (half-deflection)

G = \frac{R S}{R - S}; k = \frac{E}{( R + G ) θ}

S =

shunt for half deflection;

k =

figure of merit (A/division)

🚫 Examiner Trap · Electricity experiments

(1) Keep the metre-bridge balance point near the

centre

— there end-corrections & contact resistance matter least. (2) Balance is a

null

method, so galvanometer calibration & cell emf don't affect the result. (3) Don't pass current for long (heats the wire, changes

ρ

). (4) Figure of merit k: smaller k

\Rightarrow

more sensitive galvanometer.

Optics Experiments

Focal length (u–v)

lens: \frac{1}{v} - \frac{1}{u} = \frac{1}{f}; mirror: \frac{1}{v} + \frac{1}{u} = \frac{1}{f}

locate the image by removing parallax against a reference pin

Graph of 1/v versus 1/u: a straight line whose intercepts on both axes equal 1 over the focal length — Both intercepts of $\frac{1}{v}$ – $\frac{1}{u}$ give $\frac{1}{∣ f ∣}$ .

Refractive index (slab)

n = \frac{real depth}{apparent depth} = \frac{t}{t - shift}

travelling microscope;

t =

slab thickness

Prism — deviation & index

δ = i_{1} + i_{2} - A; n = \frac{sin \frac{A + δ _{m}}{2}}{sin \frac{A}{2}}

δ_{m}

at symmetric passage

i_{1} = i_{2}

r_{1} = r_{2} = A /2

U-shaped graph of angle of deviation versus angle of incidence for a prism, with the minimum deviation delta-m occurring when i1 equals i2 — $δ$ –i curve: minimum $δ_{m}$ at $i_{1} = i_{2}$ .

🚫 Examiner Trap · Optics experiments

(1) u,v carry

signs

; plotting

1/ v

1/ u

gives a straight line with both intercepts

1/∣ f ∣

. (2) Prism

δ

minimum

only for symmetric passage; at the minimum the ray inside is

∥

to the base. (3) Apparent depth

<

real depth; index

=

real/apparent. (4) Remove parallax to fix the image — don't just 'look sharp'.

Electronics Experiments

p–n junction diode I–V

▸ $Forward$ : negligible current until the knee (Si 0.7, Ge $0.3$ V), then mA — use a $milliammeter$ .
▸ $Reverse$ : tiny constant $μ$ A — use a $microammeter$ .
▸Dynamic resistance $r_{d} = Δ V /Δ I$ from the slope.

Zener

▸Operated in $reverse$ bias; at breakdown current rises sharply while $V_{z}$ stays constant.
▸ $V_{z} =$ the knee of the reverse curve.

Comparative: component identification

Component	Behaviour
Resistor	Ohmic — conducts both ways, $V \propto I$
Diode	Conducts one way (forward) only
LED	One-way $+$ glows when forward biased
Capacitor	Blocks steady DC (momentary charge only)

🚫 Examiner Trap · Electronics experiments

(1) Use a

milliammeter

for forward (mA) but a

microammeter

for reverse (

μ

A) — wrong meter ruins the reading. (2) Zener is read in

reverse

bias; its

V_{z}

is the reverse knee. (3) Identify by polarity test: resistor conducts both ways, diode/LED one way (LED lights), capacitor passes only a

momentary

charging current. (4) Always limit current with a series resistor to protect the diode.

More JEE Main Physics formula sheets

Frequently Asked Questions

What are the most important Experimental Skills formulas for JEE Main?

This Experimental Skills formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Vernier calipers usage, Screw gauge usage, Simple pendulum experiments, Metre scale - principle of moments, Young's modulus determination — each shown with the key result and, where useful, a worked example.

Is this Experimental Skills formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

How should I revise Experimental Skills formulas?

Blurt the Experimental Skills formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Also useful: all formula sheets · JEE Main previous-year papers · most important chapters.