Which of the following statements does not represent ohm's law?

Question

BlackTom AI · Accepted Answer

Ohm's law is V = I·R, so the potential difference (voltage) across a conductor is proportional to the current through it with the constant of proportionality equal to the resistance.

1) Relevant concepts
- V = I·R is the standard form of Ohm’s law.
- Rearranged forms: I = V/R and R = V/I.
- For an ohmic conductor, V/I (resistance) is constant; equivalently I/V (conductance) is constant.
- Units check: V (volts), I (amperes), R (ohms = V/A).

2) Step-by-step reasoning
- Start from V = I·R.
- Solve for I: I = V / R. This is the correct expression for current in terms of voltage and resistance.
- Solve for R: R = V / I. This shows V/I is constant (resistance) for an ohmic device.
- Take reciprocal: I / V = 1 / R, also a constant (conductance) for an ohmic device.

3) Intermediate calculations and unit check
- From I = V/R, units: I (A) = V (V) ÷ R (V/A) = A, consistent.
- For the incorrect form I = R·V, units would be: R·V = (V/A)·V = V^2/A, which is not amperes — so that form is dimensionally wrong.

4) Why the correct answer is correct
- Option (a) states I = R × V, which contradicts V = I·R and is dimensionally inconsistent. The correct relation between I, V, and R is I = V/R, not I = R·V.

5) Why the other options are incorrect/why they do represent Ohm’s law
- (b) V / I = constant: equivalent to R = V/I — represents Ohm’s law.
- (c) I / V = constant: equivalent to conductance = 1/R — also valid for an ohmic conductor.
- (d) V = I × R: the standard statement of Ohm’s law — correct.

Conclusion: Option a is the statement that does not represent Ohm’s law. This matches the provided answer: a.

Which of the following statements does not represent ohm's law?单项选择题

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