Experimental Skills (JEE-specific 18 experiments)

Measurement Instruments

Vernier Caliper: Measures length with least count LC = 1 MSD - 1 VSD. For standard calipers: LC = 1 mm - 0.9 mm = 0.1 mm = 0.01 cm. Reading = MSR + (VSR x LC). Zero error: if the zero of vernier doesn't coincide with zero of main scale. Positive zero error (zero of VS is to the right of zero of MS): subtract correction. Negative zero error (zero of VS is to the left): add correction. Correction = +(n x LC) for negative error and -(n x LC) for positive error, where n is the vernier division coinciding with a main scale division.

Screw Gauge (Micrometer): LC = pitch/number of circular scale divisions. Typically: pitch = 0.5 mm, 50 divisions, LC = 0.01 mm = 0.001 cm. Reading = MSR + (CSR x LC). Zero error: thimble zero above index line = negative error, below = positive error. Screw gauge has higher precision than vernier caliper by one order of magnitude.

Mechanics Experiments

Simple pendulum: T = 2*$\pi$$\sqrt{L/g}$.
Plot $T^{2}$ vs L: straight line through origin with slope = 4$\pi$²/g. Measure time for 20-50 oscillations to reduce timing error.
Effective length = string length + radius of bob. Sources of error: air resistance, finite amplitude (T increases slightly for $\theta$ > 5 degrees), parallax in length measurement.

Young's modulus (Searle's apparatus): Y = (FL)/(A$\delta_{L}$) = (MgL)/($\pi$$r^{2}$*$\delta_{L}$).
Plot stress vs strain: slope = Y. Two identical wires used — reference wire compensates for temperature expansion. Measure extension with micrometer screw. Y for steel ≈ 2 x $10^{11}$ Pa.

Surface tension (capillary rise): T = ($\rho$gr*h)/2, where r = capillary radius, h = rise height. Correction for meniscus: use h + r/3. Measure radius using traveling microscope.

Coefficient of viscosity (Stokes' law): $\eta$ = 2*$r^{2}$*($\rho_{s}$ - $\rho_{l}$)g/(9$v_{terminal}$). Drop a small sphere in a viscous liquid, measure terminal velocity over a marked distance. Sphere must be small enough for laminar flow (Re < 0.1).

Specific heat (method of mixtures): $m_{s}$$c_{s}$($T_{s}$ - $T_{f}$) = $m_{w}$$c_{w}$($T_{f}$ - $T_{w}$) + $m_{cal}$$c_{cal}$($T_{f}$ - $T_{w}$). Account for water equivalent of calorimeter. Minimize heat loss by stirring and using an insulated vessel.

Electrical Experiments

Metre bridge (Wheatstone bridge): Uses the principle $\frac{R_{1}}{R_{2}}$ = $\frac{l_{1}}{l_{2}}$, where $l_{1}$ and $l_{2}$ = (100 - $l_{1}$) are the balancing lengths.
Unknown resistance X = R*(100-l)/l, where R is the known resistance. For best sensitivity, the null point should be near the middle (l ≈ 50 cm). End corrections account for resistance of thick copper strips at the ends.

Potentiometer: A uniform wire of length L carries steady current.
V = (E/L)l (potential is proportional to length).
Two applications: (1) Compare EMFs: $\frac{E_{1}}{E_{2}}$ = $\frac{l_{1}}{l_{2}}$.
(2) Internal resistance: r = R($\frac{l_{1}}{l_{2}}$ - 1), where $l_{1}$ is null length with cell in open circuit, $l_{2}$ with cell connected to external resistance R. Advantages over voltmeter: draws no current at null point (true EMF measurement).

Galvanometer resistance (half-deflection method): Connect galvanometer with high resistance R in series. Note deflection $\theta$. Insert shunt S to get $\frac{\theta}{2}$. Then G = (R*S)/(R-S). Approximation: if R >> S, then G ≈ S. The approximation works because R >> G in typical setups.

Optics Experiments

Focal length of concave mirror: Using u-v method. Plot 1/v vs 1/u: intercepts give 1/f. Or plot u vs v: intersection with line u=v gives C (center of curvature), so f = C/2. Parallax method for image location. For best accuracy, take multiple readings with object beyond f.

Focal length of convex lens: Displacement method: for a fixed screen-object distance D > 4f, two lens positions give sharp images. f = ($D^{2}$ - $d^{2}$)/(4D), where d is the distance between the two lens positions. Also: 1/f = 1/v - 1/u (sign convention: all distances from optical center, real = positive for v, negative for u in our convention).

Refractive index of glass prism: n = sin((A+$D_{m}$)/2)/sin(A/2), where A is the prism angle and $D_{m}$ is the minimum deviation angle.
At minimum deviation, the ray passes symmetrically (i = e, $r_{1}$ = $r_{2}$ = A/2). Plot deviation vs incidence angle to find $D_{m}$ at the minimum.

Speed of sound (resonance tube): First resonance at $l_{1}$ = $\frac{\lambda}{4}$ - e (end correction), second at $l_{2}$ = 3*$\frac{\lambda}{4}$ - e.
So $\lambda$ = 2*($l_{2}$ - $l_{1}$), and v = f*$\lambda$.
End correction e = ($l_{2}$ - 3*$l_{1}$)/2. This eliminates the need to know the end correction separately.

Semiconductor Experiments

I-V characteristics of ohmic and non-ohmic conductors: Ohmic (wire): linear I-V, constant resistance. Non-ohmic (filament bulb): curved I-V, resistance increases with temperature. Plot V vs I; slope at any point gives dynamic resistance.

Diode, LED, and Zener characteristics: Forward bias: negligible current until threshold (0.7 V Si), then exponential rise. Reverse bias: tiny saturation current until breakdown. LED: similar to diode but threshold depends on color (1.5-3 V). Zener: sharp, well-defined reverse breakdown at $V_{Z}$.

Transistor characteristics: Input characteristics: plot $I_{B}$ vs $V_{BE}$ at constant $V_{CE}$. Output characteristics: plot $I_{C}$ vs $V_{CE}$ at constant $I_{B}$. Three regions: cutoff, active, saturation.
Current gain $\beta$ = $\frac{\Delta_{I_C}}{\Delta_{I_B}}$ from output characteristics.

Logic gates verification: Build OR, AND, NOT, NAND, NOR gates using diodes/transistors. Verify truth tables by applying high/low inputs and measuring output voltage. Digital IC (7400 series) may be used.

The key problem-solving concept is error analysis: every experimental result requires understanding the least count, zero error, systematic vs random errors, and how to minimize uncertainty through proper technique and repeated measurements.

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