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According to Ohm's law, the electric current I passing through a conductor is increased in such a way that the dimensions of the conductor and its temperature remain constant. Then the resistance R of the conductor _____.

Asked in GSEB Board July 2021 · Ohm's law and resistivity

• (1) remains constant
• (2) decreases
• (3) increases
• (4) initially decreases and then increases

Step-by-step solution

Why the other options are wrong

• (2) Reads R = V/I as if V stayed fixed while I grew. In fact I can rise only because V rises in the same proportion, so V/I does not change.
• (3) A resistance rises only when the conductor heats up or changes shape. Here the temperature and the dimensions are held fixed, so nothing in ρℓ/A changes.
• (4) Nothing in R = ρℓ/A changes, so there is no mechanism for a fall followed by a rise; R keeps one value throughout.

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