Understanding Ohm’s Law and Its Limits

Ohm’s law scalar forms: V=IR and I=GV

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.

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Resistance and conductance as constants

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