Drift Velocity and Current Density
Under an applied electric field $\vec{E}$, conduction electrons drift with average velocity:
$$\vec{v}_d = -\frac{e\vec{E}}{m}\tau$$
Where $\tau$ is relaxation time between successive collisions.
- Relation with Current: $I = n e A v_d$
- Current Density ($J$): $J = \frac{I}{A} = n e v_d$
- Microscopic Ohm's Law: $\vec{J} = \sigma \vec{E} = \frac{1}{\rho}\vec{E}$
Kirchhoff's Laws & Wheatstone Bridge
- Kirchhoff's Current Law (KCL - Junction Rule): The algebraic sum of currents meeting at any electrical node is zero ($\sum I = 0$, based on conservation of charge).
- Kirchhoff's Voltage Law (KVL - Loop Rule): In any closed electrical mesh, the algebraic sum of changes in potential is zero ($\sum \Delta V = 0$, based on conservation of energy).
- Balanced Wheatstone Bridge Condition:
$$\frac{P}{Q} = \frac{R}{S} \implies I_G = 0$$
