Important JEE Experiments - Quick Reference

Prerequisites

Before studying this topic, make sure you understand:

• Vernier Caliper - Precision measurement
• Screw Gauge - Micrometer measurements
• Relevant theory chapters for each experiment

The Hook: Why Practical Experiments Matter for JEE

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Mechanics Experiments

1. Vernier Caliper - Measuring Diameter/Thickness

Apparatus:

• Vernier caliper
• Object (cylinder, sphere, rectangular block)

Formula:

$$\text{Reading} = \text{MSR} + \text{VC} \times \text{LC}$$ $$\text{Actual} = \text{Observed} - \text{Zero Error}$$

Least Count: 0.01 cm (standard)

Common Errors:

• Zero error (positive/negative)
• Parallax error
• Loose jaws

JEE Focus:

• Zero error calculation ⭐⭐⭐
• Least count problems ⭐⭐⭐
• Error correction ⭐⭐⭐

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2. Screw Gauge - Wire/Sheet Thickness

Apparatus:

• Screw gauge (micrometer)
• Thin wire or metal sheet

Formulas:

$$\text{Pitch} = \frac{\text{Distance}}{\text{Rotations}}$$ $$\text{LC} = \frac{\text{Pitch}}{\text{Divisions}}$$ $$\text{Reading} = \text{LSR} + \text{CSR} \times \text{LC}$$

Least Count: 0.01 mm = 0.001 cm

Common Errors:

• Zero error
• Backlash error (rotate one direction only!)
• Over-tightening (use ratchet)

JEE Focus:

• Pitch vs LC distinction ⭐⭐⭐
• Backlash error concept ⭐⭐
• Negative zero error ⭐⭐⭐

Interactive Demo: Visualize Dimensional Analysis

Explore how units and dimensions are used to verify experimental formulas and detect errors.

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3. Simple Pendulum - Finding g

Apparatus:

• Pendulum bob, string
• Meter scale, stopwatch
• Clamp stand

Formula:

$$T = 2\pi\sqrt{\frac{L}{g}}$$ $$g = \frac{4\pi^2 L}{T^2}$$

where:

• T = time period (measured for 20 oscillations ÷ 20)
• L = effective length (string length + bob radius)

Graph: $T^2$ vs $L$ → Straight line

$$\text{Slope} = \frac{4\pi^2}{g}$$

Common Errors:

• Starting stopwatch too early/late
• Not measuring for multiple oscillations
• Forgetting to add bob radius to length
• Amplitude too large (use small angle ~5-10°)

JEE Focus:

• Graph interpretation ⭐⭐⭐
• Error minimization ⭐⭐
• Effect of amplitude ⭐⭐

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4. Meter Bridge - Unknown Resistance

Apparatus:

• Meter bridge, resistance box
• Unknown resistance, galvanometer
• Battery, key, connecting wires

Formula:

$$\frac{R}{S} = \frac{l}{100-l}$$

where:

• R = unknown resistance
• S = standard resistance (from box)
• l = balancing length

$$R = S \times \frac{l}{100-l}$$

Balance Point: Galvanometer shows zero deflection

Best accuracy: Balancing length around 40-60 cm

Common Errors:

• End resistance (use different values of S)
• Contact resistance
• High resistance in connections

JEE Focus:

• Balance point calculation ⭐⭐⭐
• Why l should be ~50cm ⭐⭐
• Graph of R vs l ⭐⭐

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5. Potentiometer - EMF and Internal Resistance

Apparatus:

• Potentiometer (wire), battery, rheostat
• Standard cell, unknown cell
• High resistance, galvanometer, key

Formulas:

EMF measurement:

$$\frac{E_1}{E_2} = \frac{l_1}{l_2}$$

Internal resistance:

$$r = \left(\frac{l_1 - l_2}{l_2}\right) R$$

where:

• $l_1$ = balancing length (key open)
• $l_2$ = balancing length (key closed with resistance R)

Common Errors:

• Primary circuit current too low/high
• Loose connections
• Potentiometer wire not uniform

JEE Focus:

• EMF ratio calculations ⭐⭐⭐
• Internal resistance formula ⭐⭐⭐
• Why potentiometer better than voltmeter ⭐⭐

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Optics Experiments

6. Focal Length of Convex Lens - u-v Method

Apparatus:

• Convex lens, optical bench
• Object pin, image screen
• Meter scale

Formula:

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Sign convention:

• u = negative (object on left)
• v = positive (real image on right)
• f = positive (convex lens)

Graph: $\frac{1}{v}$ vs $\frac{1}{u}$ → Straight line

$$\text{Slope} = -1$$ $$\text{Intercepts} = \frac{1}{f}$$

Common Errors:

• Parallax not removed properly
• Index correction ignored
• Wrong sign convention

JEE Focus:

• Sign conventions ⭐⭐⭐
• Graph interpretation ⭐⭐⭐
• Lens formula applications ⭐⭐⭐

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7. Focal Length - Displacement Method

Formula:

$$f = \frac{D^2 - d^2}{4D}$$

where:

• D = fixed distance (object to screen)
• d = distance between two lens positions
• Condition: D > 4f

Advantages:

• No parallax error
• More accurate
• Doesn’t need u, v separately

JEE Focus:

• Bessel’s method formula ⭐⭐
• Condition D > 4f ⭐⭐

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8. Prism - Angle and Refractive Index

Apparatus:

• Glass prism, drawing board
• Pins, protractor

Formulas:

Angle of prism A:

$$A = \frac{r_1 + r_2}{2}$$

Refractive index:

$$n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$

where $\delta_m$ = minimum deviation angle

Graph: $\delta$ vs $i$ → U-shaped, minimum at $\delta_m$

Common Errors:

• Prism not in minimum deviation position
• Angle measurement error
• Base of prism not on paper

JEE Focus:

• Minimum deviation formula ⭐⭐⭐
• Graph shape ⭐⭐
• Why minimum deviation preferred ⭐⭐

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9. Concave Mirror - Focal Length

Methods:

1. u-v method: Same as lens
2. Distant object method: f = radius of curvature / 2

Formula:

$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$

Note: Both u and v negative for real images

Common Errors:

• Parallax in locating image
• Index error in scale
• Mirror not vertical

JEE Focus:

• Sign conventions ⭐⭐⭐
• Mirror equation ⭐⭐⭐

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Advanced Experiments

10. Sonometer - Frequency/String Relations

Apparatus:

• Sonometer, tuning fork
• Bridges, weights, pulley

Formulas:

Fundamental frequency:

$$f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$$

where:

• L = vibrating length
• T = tension (= Mg)
• μ = mass per unit length

Relations:

• $f \propto \frac{1}{L}$ (constant T)
• $f \propto \sqrt{T}$ (constant L)

Graphs:

• $f$ vs $\frac{1}{L}$ → Straight line through origin
• $f^2$ vs $T$ → Straight line through origin

JEE Focus:

• String relations ⭐⭐
• Graph interpretation ⭐⭐

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11. Young’s Double Slit - Wavelength of Light

Apparatus:

• Laser/monochromatic source
• Double slit, screen
• Traveling microscope

Formula:

$$\lambda = \frac{\beta \cdot d}{D}$$

where:

• λ = wavelength
• β = fringe width (distance between consecutive bright/dark fringes)
• d = slit separation
• D = slit-to-screen distance

Measurement:

$$\beta = \frac{\text{Distance for n fringes}}{n}$$

Common Errors:

• Fringes not clear (adjust source distance)
• Slit separation not uniform
• Parallax in microscope

JEE Focus:

• Fringe width formula ⭐⭐⭐
• Effect of changing D, d, λ ⭐⭐⭐
• Conditions for clear fringes ⭐⭐

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12. Ohm’s Law - V-I Characteristics

Apparatus:

• Resistance wire/resistor
• Battery, ammeter, voltmeter
• Rheostat, key

Formula:

$$V = IR$$ $$R = \frac{V}{I} = \text{slope of V-I graph}$$

Graph: V vs I → Straight line through origin (for ohmic conductor)

Non-ohmic: Diode, LED (curved graph)

Common Errors:

• Zero error in ammeter/voltmeter
• Heating of wire (take quick readings)
• Loose connections

JEE Focus:

• Ohmic vs non-ohmic ⭐⭐⭐
• Graph interpretation ⭐⭐⭐
• Resistance calculation ⭐⭐

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13. Resistivity of Wire

Apparatus:

• Wire of unknown material
• Meter scale, screw gauge
• Battery, ammeter, voltmeter, rheostat

Formula:

$$\rho = \frac{RA}{L}$$

where:

• R = resistance (from V/I)
• A = cross-sectional area = $\pi r^2$
• r = radius (from screw gauge)
• L = length of wire

Procedure:

1. Find R using V-I graph (slope)
2. Measure diameter using screw gauge → find r
3. Measure length L
4. Calculate ρ

JEE Focus:

• Resistivity formula ⭐⭐⭐
• Area calculation from diameter ⭐⭐
• Units (Ω·m) ⭐⭐

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Quick Reference Tables

Measurement Instruments

Instrument	Measures	Range	Least Count
Vernier Caliper	Length, diameter, depth	0-15 cm	0.01 cm
Screw Gauge	Thickness, wire diameter	0-2.5 cm	0.001 cm
Meter Scale	Length	0-100 cm	0.1 cm
Spherometer	Radius of curvature	-	0.001 cm

Common Formulas

Experiment	Key Formula	Graph
Simple Pendulum	$g = 4\pi^2 L/T^2$	$T^2$ vs $L$ (straight)
Meter Bridge	$R = S \cdot l/(100-l)$	-
Lens	$1/f = 1/v - 1/u$	$1/v$ vs $1/u$ (slope -1)
Prism	$n = \sin[(A+\delta_m)/2] / \sin(A/2)$	$\delta$ vs $i$ (U-shaped)
YDSE	$\lambda = \beta d/D$	-
Ohm’s Law	$V = IR$	$V$ vs $I$ (straight)

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Common Sources of Error

Systematic Errors

1. Zero error: Vernier caliper, screw gauge, meters
2. Index error: Optical bench, scales
3. Backlash error: Screw gauge
4. Least count limitation: All instruments

How to minimize:

• Always check and correct for zero error
• Use better instruments (smaller LC)
• Proper calibration

Random Errors

1. Parallax: Reading scales at angle
2. Human reaction time: Stopwatch measurements
3. Fluctuating readings: Electrical measurements

How to minimize:

• Take multiple readings (≥3)
• Calculate mean value
• Remove eye at level with scale
• Use fiducial marks

Personal Errors

1. Improper technique: Not following procedure
2. Carelessness: Misreading scales
3. Bias: Forcing readings to match expected value

How to avoid:

• Follow standard procedure
• Double-check readings
• Be objective in observations

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JEE Viva Questions - High Frequency

Vernier Caliper

Q: Why is it called “vernier”? A: Named after Pierre Vernier (1631) who invented the scale

Q: Can we measure depth with vernier caliper? A: Yes, using the depth probe

Q: How to find least count? A: LC = 1 MSD / n (number of VS divisions) = 0.01 cm

Q: What if zero error is positive? A: Reading shows more than actual, so subtract error

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Screw Gauge

Q: What is pitch? A: Distance moved by screw in one complete rotation (usually 0.5 mm)

Q: What is backlash error? How to avoid? A: Error due to loose threads. Avoid by rotating in one direction only.

Q: Why is screw gauge more precise than vernier? A: Converts rotation to small linear motion, LC = 0.001 cm vs 0.01 cm

Q: Can pitch be changed? A: No, it’s fixed by screw thread design

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Simple Pendulum

Q: Why measure for 20 oscillations? A: To minimize human reaction time error in using stopwatch

Q: What is effective length? A: String length from point of suspension to center of bob = L + r (bob radius)

Q: Why should amplitude be small? A: Formula $T = 2\pi\sqrt{L/g}$ valid only for small angles (< 10°)

Q: Does mass of bob affect time period? A: No, T is independent of mass

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Meter Bridge

Q: Why is it called “meter bridge”? A: Uses 1-meter (100 cm) long wire

Q: Why should balancing length be near 50 cm? A: Maximum accuracy, minimum percentage error

Q: What is end resistance? A: Resistance at wire ends and connections, causes error

Q: Based on which principle? A: Wheatstone bridge principle

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Potentiometer

Q: Advantage over voltmeter? A: Draws no current at balance, measures true EMF (not terminal voltage)

Q: Why is primary circuit kept on continuously? A: To maintain constant potential gradient along wire

Q: What if null point not found? A: Either EMF too high or primary current too low; adjust rheostat

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Optical Experiments

Q: What is parallax? A: Apparent shift in position when viewed from different angles

Q: How to remove parallax? A: Adjust until object and image/mark appear at same position from all angles

Q: Why use minimum deviation in prism? A: Most accurate, symmetric ray path, easy to locate

Q: Real vs virtual image? A: Real: can be caught on screen, formed by actual convergence. Virtual: cannot be caught, formed by apparent divergence

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Memory Tricks for Experiments

Apparatus Checklist

“BORC-GK” for electrical experiments:

• Battery
• Ohmmeter/other meters
• Rheostat
• Connecting wires
• Galvanometer (if needed)
• Key

Graph Patterns

Straight lines:

• $T^2$ vs $L$ (pendulum)
• $1/v$ vs $1/u$ (lens)
• $V$ vs $I$ (Ohm’s law)
• $f$ vs $1/L$ (sonometer)

Curves:

• $\delta$ vs $i$ (prism - U-shaped)
• $I$ vs $V$ (diode - exponential)

Sign Conventions

“Real is Positive, Virtual is Negative” (lens/mirror)

Lens:

• Object left (u = -)
• Real image right (v = +)
• Virtual image left (v = -)

Mirror:

• Everything on same side
• Real image: v = -
• Virtual image: v = +

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JEE Strategy: Experiment-Based Questions

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Related Topics

Within Experimental Skills

• Vernier Caliper - Detailed measurement technique
• Screw Gauge - Precision measurement theory

Theory Chapters Referenced

Experiment	Theory Chapter
Simple Pendulum	Oscillations
Meter Bridge	Current Electricity
Potentiometer	Current Electricity
Lens/Mirror	Optics
Prism	Optics
YDSE	Wave Optics
Sonometer	Waves

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Teacher’s Summary

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