Current Electricity ↔ Electrostatics: The electric field E that drives drift velocity in Current Electricity is the same E from Coulomb's law. V = IR at the macroscopic scale mirrors E·d = potential difference at the microscopic scale. Capacitors (Electrostatics) and resistors (Current Electricity) have exactly opposite combination rules.

Current Electricity ↔ Magnetism: Current-carrying conductors produce magnetic fields (Biot-Savart law). The force on a current-carrying wire in a magnetic field (F = BIl) uses the same I defined here. Moving charges (current) create magnetism.

Current Electricity ↔ Electromagnetic Induction: Changing magnetic flux induces EMF (Faraday's law). The induced EMF drives current through the circuit resistance, exactly as a cell's EMF does. V = ε − Ir applies equally to induced EMF circuits.

Current Electricity ↔ Semiconductors: The temperature dependence of resistance (α < 0 for semiconductors) is the basis of diodes, transistors, and all modern electronics. Resistivity ρ = m/($ne^{2}$τ) links the carrier concentration n (semiconductor physics) to circuit behavior.

Current Electricity ↔ Thermodynamics: Joule heating H = $I^{2}$Rt is the conversion of electrical energy to thermal energy. This is the First Law of Thermodynamics applied to electrical systems. Efficiency = P_external/P_total connects to thermodynamic efficiency concepts.

Current Electricity ↔ Modern Physics: The resistivity formula ρ = m/($ne^{2}$τ) uses the electron mass m and charge e — quantum mechanical quantities. The Drude model (classical free electron theory) is a precursor to quantum mechanics of solids.