EQ-OHM · Electrical Circuits
Ohm's Law
-I*R + V = 0
Variables
variable
I
current through the conductor
- Object
- conductor
- Property
- ElectricCurrent
- Context
- steady_state
variable
R
resistance (material- and geometry-dependent)
- Object
- resistor
- Property
- Resistance
- Context
- steady_state
variable
V
potential difference across the conductor
- Object
- conductor
- Property
- ElectricPotentialDifference
- Context
- steady_state
Axioms
algebraic classical commutative_factors constant_coefficients deterministic linear steady_state
Assumptions
- Linear (ohmic) material: R is independent of V, I, and temperature in the operating regime
- Steady state (no significant dV/dt or dI/dt effects)
- Scalar currents / voltages (no anisotropy or tensorial resistivity)
Derivation
- Empirical; Ohm (Die galvanische Kette, 1827)
- Derivable from the Drude model: linear response of free electrons to an applied field under collision-dominated transport
- Microscopically: J = σE with σ = ne²τ/m (τ = mean free time), then V = ∫E·dl and I = ∫J·dA yields V = IR for a uniform conductor
References
- Jackson, Classical Electrodynamics, 3rd ed., §5.18
- Ashcroft & Mermin, Solid State Physics, Ch. 1