Summary

• Ohm’s Law: $V = IR$, where $V$ is potential difference, $I$ is current, $R$ is resistance. Valid for ohmic materials at constant temperature.
• Resistivity: $\rho = \frac{RA}{L}$, depends on material and temperature. For metals, $\rho_T = \rho_0 [1 + \alpha (T - T_0)]$.
• Conductivity: $\sigma = \frac{1}{\rho} = ne\mu$, where $n$ is charge carrier density, $e$ is charge, $\mu$ is mobility.
• Drift velocity: $v_d = \frac{I}{neA} = \frac{eE\tau}{m}$, with $\tau$ as relaxation time.
• Resistors in series: $R_{eq} = R_1 + R_2 + \dots$; same current, voltage divides.
• Resistors in parallel: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$; same voltage, current divides.
• Kirchhoff’s Laws:
  • Junction rule: $\sum I_{in} = \sum I_{out}$ (charge conservation).
  • Loop rule: $\sum \Delta V = 0$ (energy conservation).
• Wheatstone bridge: Balanced when $\frac{R_1}{R_2} = \frac{R_3}{R_4}$, giving zero current through galvanometer.
• Meter bridge: Uses slide wire to find unknown resistance via null point; $\frac{R}{S} = \frac{l}{100-l}$.
• Potentiometer: Measures emf without drawing current; $E \propto l$ for constant current.
• Internal resistance: $r = \left(\frac{E}{V} - 1\right)R$, where $V$ is terminal voltage across load $R$.
• Power dissipation: $P = I^2R = \frac{V^2}{R} = VI$ (Joule heating).
• Cell combinations: Series gives higher voltage; parallel gives higher current capacity; mixed grouping optimizes power.

Physical quantities, symbols, dimensions and units used in this chapter.