Current: $I = \frac{Q}{t} = neAv_d \quad [\text{A}]$

Drift Velocity: $v_d = \frac{eE\tau}{m} = \frac{I}{neA} \quad [\text{LT}^{-1}]$

Current Density: $J = \frac{I}{A} = nev_d = \sigma E \quad [\text{AL}^{-2}]$

Resistance and Resistivity: $R = \frac{V}{I} = \frac{\rho l}{A} \quad [\text{ML}^2\text{T}^{-3}\text{A}^{-2}]$ $\rho = \frac{RA}{l} = \frac{m}{ne^2\tau} \quad [\text{ML}^3\text{T}^{-3}\text{A}^{-2}]$ $\sigma = \frac{1}{\rho} = \frac{ne^2\tau}{m} \quad [\text{M}^{-1}\text{L}^{-3}\text{T}^3\text{A}^2]$

Temperature Dependence: $R = R_0(1 + \alpha \Delta T) \quad \alpha \text{ in [K}^{-1}\text{]}$

Power and Energy: $P = VI = I^2R = \frac{V^2}{R} \quad [\text{ML}^2\text{T}^{-3}]$ $W = VIt = I^2Rt \quad [\text{ML}^2\text{T}^{-2}]$

EMF and Terminal Voltage: $V = \varepsilon - Ir \text{ (discharge)}; \quad V = \varepsilon + Ir \text{ (charge)} \quad [\varepsilon] = [\text{ML}^2\text{T}^{-3}\text{A}^{-1}]$

Maximum Power Transfer: $P_{\max} = \frac{\varepsilon^2}{4r} \text{ when } R = r$

Kirchhoff's Signs: $\Delta V_{\text{(resistor, with I)}} = -IR; \quad \Delta V_{\text{(cell, - to +)}} = +\varepsilon$

Wheatstone Bridge: $\frac{P}{Q} = \frac{R}{S} \Rightarrow I_g = 0$

Metre Bridge: $\frac{R}{S} = \frac{l}{100-l}; \quad l' = 100 - l \text{ (on interchange)}$

Potentiometer: $\frac{\varepsilon_1}{\varepsilon_2} = \frac{l_1}{l_2}; \quad r = R\!\left(\frac{l_1 - l_2}{l_2}\right); \quad \varepsilon = kl$

Joule Heating: $H = I^2Rt \quad [\text{ML}^2\text{T}^{-2}]$

Series/Parallel Ratio: $\frac{P_{\text{parallel}}}{P_{\text{series}}} = n^2 \text{ (n identical resistors, same battery)}$