Ohm’s law scalar forms: V=IR and I=GV

Summary

Ohm’s law gives the relationship between voltage (V), current (I), and resistance (R) in an ohmic conductor where resistance is constant. In scalar form it is written as V = IR, meaning the voltage across two points is directly proportional to the current through the conductor, with resistance as the proportionality constant. The reciprocal quantity, conductance G (where G = 1/R), allows an equivalent scalar form: I = GV, expressing that current is directly proportional to voltage with conductance as the proportionality constant. These forms apply when the conductor behaves ohmically (R constant and independent of current) and are used in circuit analysis for resistive circuits. If resistance is not constant, the simple V = IR (or I = GV) relationship no longer qualifies as Ohm’s law, though it can still be used to define a static/DC resistance. In more general physics contexts, Ohm’s law can be extended beyond scalar circuit forms (e.g., to field-based or vector forms), but the scalar versions above are the standard circuit relationships.

Key Points

• 1

  Ohm’s law scalar forms relate voltage, current, resistance, and conductance: V = IR and equivalently I = GV.

• 2

  The equivalence uses conductance G = 1/R, so both forms express the same proportional relationship.

• 3

  These scalar forms assume an ohmic conductor with constant resistance; if resistance varies with current, the simple Ohm’s law form does not strictly apply.