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Not all circuits obey Ohm's Law; in fact, most don't!

Ohm's Law is a law of constant proportionality, and states that 'the current flowing through a conductor is directly-proportional to the potential difference across the ends of that conductor providing physical conditions, such as temperature, remain constant'. Expressed another way, the ratio of voltage to current must be a constant for variations in voltage, for Ohm's Law to apply.

Ohm's Law only applies to linear ('ohmic') materials which includes metals, providing their temperatures are constant. Electrolytes, gases, semiconductors, however are non-linear ('non-ohmic'), and Ohm's Law doesn't apply to these.

The ratio of voltage to current is resistance, and this applies to all circuits, whether linear or non-linear. But it only tells us what the resistance happens to be at that particular ratio. But for Ohm's Law to apply, the resistance must remain constant for changes in voltage. Put simply, if the resistance of a circuit changes when the applied voltage varies, then it is not obeying Ohm's Law.

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