Ohm’s law states that the voltage drop V across an ideal resistor is linearly proportional to the current i flowing through the resister as in V = iR, where R is the resistance. However, real resistors may not always obey Ohm’s law. Suppose that you performed some very precise experiments to measure the voltage drop and corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm’s law:
i | −1 | −0.5 | −0.25 | 0.25 | 0.5 | 1 |
V | −637 | −96.5 | −20.5 | 20.5 | 96.5 | 637 |
To quantify this relationship, a curve must be fit to the data. Because of measurement error, regression would typically be the preferred method of curve fitting for analyzing such experimental data. However, the smoothness of the relationship, as well as the precision of the experimental methods, suggests that interpolation might be appropriate. Use a fifth-order interpolating polynomial to fit the data and compute V for i = 0.10.
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