Ohm’s devices — for an ideal ohmic resistor, the current–voltage (I–V) relationship is linear and passes through the origin. Does the claim “current and voltage have a nonlinear relationship” hold for ohmic conductors?

Introduction / Context:Ohm’s law states that for an ohmic conductor the voltage across it is directly proportional to the current through it at a fixed temperature and physical state. This implies a straight-line I–V characteristic through the origin. The given claim asserts nonlinearity, which is not true for ideal resistors used in introductory circuit analysis.

Given Data / Assumptions:

• Component is an ideal ohmic resistor.
• Temperature and physical conditions are constant.
• Small-signal and large-signal operation remain within the linear region.

Concept / Approach:The defining relation of an ohmic resistor is V = I * R with constant R. If R is constant, doubling I doubles V. The graph of V vs. I is a straight line with slope R. Many real devices (diodes, lamps, thermistors) are indeed nonlinear, but the ohmic resistor model is linear by definition and underpins the superposition and Thevenin/Norton techniques learned early in circuits.

Step-by-Step Solution:

Verification / Alternative check:Bench measurements with a variable supply and ammeter show linear scaling of V and I for carbon film or metal film resistors operated within ratings. SPICE resistor elements are ideal linear by default.

Why Other Options Are Wrong:

• “All elements are nonlinear”: diodes/transistors are, but ohmic resistors are modeled as linear.
• “Only at high temperature” and “depends on tolerance”: temperature and tolerance shift R but do not make the I–V relation mathematically nonlinear over the operating range.
• “Because power depends on I^2”: that does not change the linear V–I law.

Common Pitfalls:Generalizing nonlinearity from semiconductor examples to all components; confusing power formulas with I–V linearity.

Final Answer:Incorrect — ohmic resistors have a linear I–V relationship.