Test a constant-resistance claim against curved data

Establish the model and evidence

A resistance inferred from one voltage-current pair is not a test that resistance is constant. To test an ohmic model, collect several current and voltage pairs while controlling relevant conditions. Here the supplied graph places voltage on the vertical axis and current on the horizontal axis, so a straight-line slope has units V/A=Ω. Reversing the axes would make the slope conductance instead.

The original synthetic packets compare V=20I with a nonlinear response V=20I+100I³, using amperes and volts. Small fixed measurement errors and an independently adjustable common voltage offset are added. These functions are hypothetical device responses, not claims about a named material. The nonlinear packet can mimic increasing effective resistance without establishing a microscopic heating mechanism.

Allow a fitted intercept when investigating a possible zero offset. A constant offset moves the graph without changing the slope of differences. Curvature, however, changes the low-current and high-current interval slopes and leaves a structured pattern in linear-fit residuals. A fitting routine always returns a line; its existence does not establish that the line is an appropriate physical model.

For a nonlinear element, V/I at one point, a local interval slope and a global best-fit slope need not agree. Report exactly which quantity was calculated. A useful independent check could stabilize temperature, verify the voltmeter zero with no current, or repeat the current sequence in reverse to look for history dependence. The browser supplies only the declared deterministic packet, so it cannot certify those practical checks occurred.

Worked evidence

Without measurement errors, the nonlinear model gives 1.0125 V at 0.05 A and 4.8 V at 0.20 A. The ratios V/I are 20.25 Ω and 24 Ω. A +0.10 V zero offset changes both readings but cannot remove the underlying change in interval slope.

Predict and investigate

Will changing the voltage offset remove the high-current curvature from the nonlinear packet?

Compare ohmic and nonlinear packets at zero offset. Record fitted slope, residual size and two interval slopes. Then add +0.20 V to the nonlinear packet and distinguish the shifted intercept from unchanged curvature.

Transfer to changed conditions

A data packet gives V=1.0, 2.2 and 3.6 V at I=0.05, 0.10 and 0.15 A. Compare successive interval slopes and explain whether a constant voltage offset can make them equal.

Compare the worked transfer

The interval slopes are 24 Ω and 28 Ω. A common additive voltage offset cancels from each difference, so it cannot make the slopes equal. More evidence is needed to identify the cause of the nonlinearity.

Explain the boundary

Why would a single numerical resistance or a high-quality-looking line be insufficient evidence for constant resistance?

Ohmic response is conditioned on material state

Calling a response ohmic means the voltage-current relation is linear under the stated fixed material conditions. It does not generally mean resistivity is independent of temperature: many metallic conductors have larger resistivity at higher temperature. The current CED’s 11.3.B.1.ii temperature wording is therefore used only as an ideal fixed-parameter premise, not a universal property of ohmic matter. Joule heating can change those conditions.

Predict and check: at one controlled temperature, I=0.050V with amperes and volts has conductance 0.050 S and resistance 20 Ω. If a separately supplied hotter-state packet has I=0.040V, its resistance is 25 Ω; each packet is linear, but their material-state resistances differ. On I-versus-V axes the slope is 1/R, not R. A nonzero-current V/I ratio from one point is still insufficient to establish linearity over an interval. (Current clauses 11.3.A and 11.3.B.)

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original cases and computed/synthetic evidence, not actual laboratory measurements. These activities are virtual only: do not reproduce wiring, short-circuit, battery charging, heating or charged-capacitor experiments. Any real practical work requires qualified supervision and an independently approved safety procedure.

Clause-level source/action reconciliation checked 31 October 2026 against the linked current framework and Fall 2026 clarification. Added packets are original virtual comparisons; no new practical or learner-completion claim.