Measurement Instruments

$\text{LC}_{\text{Vernier}} = 1\text{ MSD} - 1\text{ VSD} \quad ; \quad \text{LC}_{\text{Screw}} = \frac{\text{pitch}}{N}$

$\text{Reading} = \text{MSR} + (n \times \text{LC}) \quad \text{(apply zero error correction)}$

Mechanics

$T = 2\pi\sqrt{\frac{l}{g}} \quad \Rightarrow \quad g = \frac{4\pi^2 l}{T^2} \quad ; \quad \text{Slope of } T^2\text{ vs }l = \frac{4\pi^2}{g}$

Y = \frac{FL}{A\Delta L} \quad [$ML^{-1}T^{-2}$]\text{, Pa} \quad ; \quad A = \frac{\pi d^2}{4}$$

S = \frac{hr\rho g}{2\cos\theta} \quad [$MT^{-2}$]\text{, N/m} \quad ; \quad v_t = \frac{2r^2(\rho-\sigma)g}{9\eta} \quad [\eta: $ML^{-1}T^{-1}$]\text{, Pa·s}$$

$m_1 l_1 = m_2 l_2 \quad \text{(Principle of Moments)}$

Waves & Thermal

v = 2f(l_2-l_1) \quad [$LT^{-1}$]\text{, m/s} \quad ; \quad e = \frac{l_2-3l_1}{2}

$m_1c_1(T_1-T) = m_2c_2(T-T_2) + m_{\text{cal}}c_{\text{cal}}(T-T_2)$

Electrical

\frac{R}{S} = \frac{l}{100-l} \quad ; \quad \rho = \frac{RA}{L} \quad [ML^3$T^{-3}A^{-2}]\text{, \Omega$·m}$$

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \quad \text{(Mirror)} \quad ; \quad \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \quad \text{(Lens)}$

$k = \frac{I}{\theta} \text{ [A/div]} \quad ; \quad G \approx S \text{ (when } S \ll R\text{)}$

Optics & Semiconductors

$\mu = \frac{\sin\!\left(\dfrac{A+\delta_{\min}}{2}\right)}{\sin\!\left(\dfrac{A}{2}\right)} \quad \text{(Prism, min deviation: }i=e\text{)}$

$\mu = \frac{\text{real depth}}{\text{apparent depth}} \quad \text{(Glass slab)}$

$V_{\text{th,Si}} \approx 0.7\text{ V} \quad ; \quad V_{\text{th,Ge}} \approx 0.3\text{ V} \quad ; \quad P_{Z,\text{max}} = V_Z I_{Z,\text{max}}$