pinned: true | type: cheat_sheet | topic: complete-quick-reference

INSTRUMENTS

• Vernier LC = 1 MSD − 1 VSD (typically 0.02 mm for 50-div)
• Screw gauge LC = pitch/divisions (typically 0.01 mm)
• Reading = MSR + (n × LC)
• +ZE → Subtract | −ZE → Add (PS-NA)
• Backlash error (screw gauge): rotate ONE direction only

MECHANICS

$T = 2\pi\sqrt{l/g} \Rightarrow \text{slope of } T^2\text{ vs }l = 4\pi^2/g$

• Effective length = string + bob radius $Y = FL/(A\Delta L); \quad S = hr\rho g/(2\cos\theta); \quad v_t = 2r^2(\rho-\sigma)g/(9\eta)$

WAVES & THERMAL

$v = 2f(l_2-l_1) \quad \text{(end correction eliminated)}$ $e = (l_2 - 3l_1)/2$ $m_1c_1\Delta T_1 = m_2c_2\Delta T_2 + m_{cal}c_{cal}\Delta T_2$

ELECTRICAL

$R/S = l/(100-l) \quad \text{(metre bridge; interchange: } l' = 100-l\text{)}$ $\rho = RA/L \quad (A = \pi d^2/4)$ $G \approx S \text{ when } S \ll R \quad \text{(half deflection method)}$

OPTICS

SEMICONDUCTORS

• Si: V_th ≈ 0.7 V | Ge: V_th ≈ 0.3 V (mnemonic: "Silicon Seven, Germanium Three")
• Zener: reverse breakdown at V_Z → constant voltage → voltage regulation
• LED: V_th ≈ 1.5–3 V; emits light in forward bias
• Color code: BB ROY of Great Britain has Very Good Wife (0–9)

ERROR RULES

1. +ZE → subtract from reading
2. Use v = 2f(l_{2}−l_{1}), not 4fl_{1} (end correction eliminated)
3. l_eff = string + bob radius for pendulum
4. A = π$d^{2}$/4 (not π$d^{2}$) for resistivity
5. Balance in 40–60 cm range for metre bridge
6. Zener needs series resistor always