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?
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AV = I * R
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BI = V / R
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CR = I * V
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DR = V / I
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EV / I = R
Answer
Correct Answer: R = I * V
Explanation
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:
Base: V = I * R.Divide both sides by R → I = V / R (valid).Divide both sides by I → R = V / I (valid).Check R = I * V → units become A * V = W (power), not Ω → invalid.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