Ohm's Law & Circuits

Ohm's Law: V = IR — the voltage across a conductor is proportional to the current through it (for ohmic materials).

Resistance R = ρL/A, where ρ is resistivity, L is length, A is cross-section area.

Resistors in series: R_total = R₁ + R₂ + R₃ + ... (current is the same through each).

Resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + ... (voltage is the same across each).

Power dissipated: P = VI = I²R = V²/R. This is Joule's law of heating.

Kirchhoff's Current Law (KCL): The sum of currents entering a junction equals the sum leaving it.

Kirchhoff's Voltage Law (KVL): The sum of potential differences around any closed loop is zero.

Internal resistance of a battery: V_terminal = EMF − Ir, where r is internal resistance.