What is the relationship between the applied voltage (ΔV), current (I) and resistance (R) of a conductor?

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Question: What is the relationship between the applied voltage (ΔV), current (I) and resistance (R) of a conductor?

Option a: R = IΔV. This rearranges the standard Ohm’s law incorrectly. It multiplies current and voltage together to equate to resistance, which has units that don’t align with this product, so this cannot be correct.

Option b: ΔV = I R. This is the standard form of Ohm’s law for a conductor, stating that the potential difference across a resistor equals the current through the resistor times its resistance. It matches the units: volts = amperes × ohms, which is consistent with V = IR.

Option c: I = ΔV R. This places R on the right-hand side multiplied by ΔV, which would give units of volt-amps, not current. It also reverses the correct proportional relationship, making it incorrect.

Option d: ΔV = I/R. This expresses voltage as current divided by resistance, which would imply ΔV = I ÷ R. That is the inverse relationship to Ohm’s law and thus does not describe the direct proportionality between voltage and current through resistance.

In summary, the correct mathematical relationship that ties ΔV, I, and R together in a single conductor is the product form ΔV = I × R, while the other options either invert, misplace, or misapply the variables, leading to incorrect units or logical structure.

UCIC 202503 PHYS101 Quiz 10

What is the relationship between the applied voltage (ΔV), current (I) and resistance (R) of a conductor?

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