1. Vernier Caliper
- LC = 1 MSD − 1 VSD = 0.02 mm (for 50 VSD = 49 MSD, 1 MSD = 1 mm)
- Reading = MSR + (coinciding VSD × LC)
- Positive zero error (Vernier zero RIGHT of main scale zero): instrument reads MORE → SUBTRACT
- Negative zero error (Vernier zero LEFT): instrument reads LESS → ADD
- Mnemonic: PS-NA (Positive-Subtract, Negative-Add)
2. Screw Gauge
- LC = pitch / no. of circular divisions = 0.5/50 = 0.01 mm (typical)
- Reading = MSR + (CSR × LC)
- Backlash error: reverse direction → screw shifts before pointer moves. Prevention: rotate in one direction
3. Simple Pendulum
- T = 2π√(l/g); vs l is linear, slope = 4π^{2}/g
- Effective length = string length + bob radius (critical!)
- Neglecting bob radius → l underestimated → g underestimated
4. Resonance Tube
- First resonance: l_{1} + e = λ/4; Second: l_{2} + e = 3λ/4
- Best formula: v = 2f(l_{2} − l_{1}) — end correction cancels
- v = 4fl_{1} is less accurate (includes end correction e)
- End correction: e = (l_{2} − 3l_{1})/2
5. Metre Bridge
- Wheatstone principle: R/S = l/(100 − l)
- Interchange R and S: new balance at l' = 100 − l
- Balance should be in 40–60 cm range for maximum accuracy
- Resistivity: ρ = RA/L (A = π/4)
6. Optics (All)
- Concave mirror: f < 0; Convex mirror: f > 0
- Convex lens: f > 0; Concave lens: f < 0
- Mirror formula: 1/v + 1/u = 1/f
- Lens formula: 1/v − 1/u = 1/f (note the subtraction)
- Prism minimum deviation (i = e): μ = sin((A+δ_min)/2)/sin(A/2)
- Glass slab: μ = real depth / apparent depth
7. Semiconductors
- Si diode: V_th ≈ 0.7 V (wider band gap ~1.1 eV)
- Ge diode: V_th ≈ 0.3 V (narrower band gap ~0.67 eV)
- Zener: reverse breakdown at V_Z → constant voltage → voltage regulation
- Zener ALWAYS needs series resistor to limit current
- LED: emits photons in forward bias; V_th ≈ 1.5–3 V
8. Critical Error Rules
- Positive zero error → subtract (not add)
- Use v = 2f(l_{2}−l_{1}), not 4fl_{1}
- Include calorimeter heat capacity in specific heat calculation
- A = π/4 for cross-sectional area (not π)