type: formula_sheet | topic: all-formulas | pinned: false

Measurement Instruments

$\text{Vernier LC} = 1\text{ MSD} - 1\text{ VSD} = \frac{1}{n}\text{ MSD} \quad [L], \text{ m}$

$\text{Reading}_{\text{Vernier}} = \text{MSR} + (n_{\text{VSD}} \times \text{LC})$

$\text{Screw Gauge LC} = \frac{\text{pitch}}{N_{\text{circular divisions}}} \quad [L], \text{ m}$

Mechanics

$T = 2\pi\sqrt{\frac{l}{g}} \Rightarrow T^2 = \frac{4\pi^2}{g}l \Rightarrow \text{slope of } T^2 \text{ vs } l = \frac{4\pi^2}{g} \quad [T], \text{ s}$

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

S = \frac{h r \rho g}{2\cos\theta} \quad [$MT^{-2}$], \text{ N/m}

v_t = \frac{2r^2(\rho - \sigma)g}{9\eta} \quad ; \quad F_{\text{Stokes}} = 6\pi\eta r v \quad [\eta: $ML^{-1}T^{-1}$], \text{ Pa·s}$$

Waves & Thermal

v_{\text{sound}} = 2f(l_2 - l_1) \quad [$LT^{-1}$], \text{ m/s}

$e = \frac{l_2 - 3l_1}{2} \quad [L], \text{ m}$

m_1 c_1 (T_1 - T) = m_2 c_2 (T - T_2) + m_{\text{cal}} c_{\text{cal}} (T - T_2) \quad [c: L^2$T^{-2}K^{-1}$], \text{ J/(kg·K)}$$

Electrical

$\frac{R}{S} = \frac{l}{100 - l} \quad \text{(Metre bridge balance)}$

\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)} \quad [$L^{-1}$], \text{ m}^{-1}

$k = \frac{I}{\theta} \quad [A/\text{div}] \quad \text{(Figure of merit)}$

Optics

$\mu = \frac{\sin\left(\frac{A + \delta_{\min}}{2}\right)}{\sin\left(\frac{A}{2}\right)} \quad \text{(Prism, at minimum deviation)}$

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

Electronics

$V_{\text{th, Si}} \approx 0.7\text{ V} \quad ; \quad V_{\text{th, Ge}} \approx 0.3\text{ V}$

$P_{Z\text{,max}} = V_Z \cdot I_{Z\text{,max}} \quad \text{(Zener power rating)}$