For the graph shown in the figure, what physical quantity does the slope of the graph represent for ohmic material?

Question

BlackTom AI · Accepted Answer

Ohm's law, V = IR, so current I is directly proportional to potential (voltage) V with proportionality 1/R.

1. Relevant knowledge points and concepts
- Ohm’s law: V = IR relates potential difference V, current I, and resistance R for an ohmic material.
- A graph of current (vertical axis) versus potential (horizontal axis) for an ohmic conductor is a straight line through the origin with slope ΔI/ΔV.
- Conductance G is defined as G = 1/R and has units siemens (S) = A/V.

2. Step-by-step reasoning
- Start from Ohm’s law: V = IR.
- Solve for I as a function of V: I = V/R.
- This has the linear form I = (1/R)·V, so the coefficient of V is the slope on an I vs V graph.

3. Calculations and intermediate steps
- I = (1/R) V implies slope m = ΔI/ΔV = 1/R.
- Units check: slope units = A/V = S (siemens) = 1/Ω, consistent with reciprocal resistance.

4. Why the correct answer is correct
- Because the plotted quantity is current versus potential and Ohm’s law gives I proportional to V with proportionality constant 1/R, the slope numerically equals the conductance, i.e., the reciprocal of the resistance.

5. Why the other options are incorrect (brief)
- Power: P = VI (units W); power is not the slope of I vs V.
- Resistivity (ρ): a material property with units Ω·m; resistivity is related to resistance by R = ρL/A and not directly the slope of an I–V graph.
- 1/(resistivity): that is conductivity σ (units S/m); slope has units S, not S/m, and the slope depends on the conductor’s geometry (length and area), so it is not simply σ.
- Resistance: R = V/I is the reciprocal of the slope, so R is not the slope but its inverse.

6. Conclusion
- Therefore the slope of the I versus V graph for an ohmic material equals 1/(resistance), which matches the provided correct answer.

For the graph shown in the figure, what physical quantity does the slope of the graph represent for ohmic material?单项选择题

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