Linear I-V characteristics

With I vertical and V horizontal,

If the axes are reversed—V vertical, I horizontal—the slope is instead R. Always read the axis definitions before interpreting a slope.

For the ideal model, doubling V doubles I and the ratio V/I remains constant. The line passes through the origin: zero applied terminal voltage gives zero current.

A straight line with a nonzero intercept is still affine, but it is not the V=RI characteristic of a resistor alone. The intercept would indicate some additional source-like behaviour or measurement offset that the resistor model does not contain.

Suppose measurements give (V,I)=(1 V,2 mA), (2 V,4 mA), (3 V,6 mA). Every point is consistent with

Using two separated points gives the same slope:

Agreement of ratio and slope is an internal check for a line through the origin.

Instrument uncertainty, resistor tolerance, contact resistance, lead resistance, electrical noise and self-heating can make measured points scatter. The engineering question is not whether every point is exact, but whether a constant-R model is adequate over the operating range of interest.

When self-heating changes R as voltage rises, the I–V curve can bend. That deviation is physical information, not automatically bad data.

Many useful devices intentionally have nonlinear I–V characteristics. A diode or transistor is not “a bad resistor”; it is a different element model.

For a nonlinear curve one may later define local or differential slopes near an operating point, but one constant R cannot represent the complete curve globally.

This is only a preview. Incremental device models belong to later electronics courses.

1. An I–V line has slope 0.25 mA/V. Find R.
2. Measured points are (1 V,1 mA), (2 V,2 mA), (4 V,4 mA). What model and R fit them?
3. A graph is a straight line but crosses I=1 mA at V=0. Is it the characteristic of an ideal resistor alone? Explain.
4. Why can self-heating bend the measured I–V curve of a physical resistor?