Spot the imposter — forms of Ohm’s law: Which of the following expressions is NOT a correct rearrangement of Ohm’s law for resistive circuits?

Introduction / Context:
Ohm’s law relates voltage, current, and resistance for ohmic conductors. Rearranging it correctly is a frequent algebraic step in design and troubleshooting. Identifying incorrect forms prevents calculation errors and misinterpretation of measurements.

Given Data / Assumptions:

• Ohm’s law base form: V = I * R.
• Linear, time-invariant, resistive element.
• SI units: volts (V), amperes (A), ohms (Ω).

Concept / Approach:

Starting from V = I * R, valid rearrangements are obtained by dividing both sides by I or R. Multiplying I and V to obtain resistance is dimensionally incorrect because I * V yields power (watts), not resistance (ohms).

Step-by-Step Solution:

Verification / Alternative check:

Dimensional check: Ω = V/A. Compare to I * V = A * V = W. Since Ω ≠ W, the expression “R = I * V” must be wrong.

Why Other Options Are Wrong:

• The other listed forms are algebraically consistent with V = I * R.
• Option E restates D; both are valid.

Common Pitfalls:

• Confusing P = I * V (power) with V = I * R (Ohm’s law).
• Plugging values into a wrong formula that happens to produce a number with wrong units.

Final Answer:

R = I * V