Ohm's Law

The idea

For many materials, the current through a conductor is proportional to the potential difference across it. Georg Ohm published this in 1827 and was ridiculed for it.

$$V=IR$$

Rearranged as needed:

$$I=\frac{V}{R}R=\frac{V}{I}$$

Worked example

A $12\mathrm{V}$ battery drives a $6.0\Omega$ resistor. What current flows?

$$I=\frac{V}{R}=\frac{12\mathrm{V}}{6.0\Omega }=2.0\mathrm{A}$$

Finding it from data, not from the formula

The point of Ohm’s Law Investigation is that you discover this relationship. Measure current at several voltages and plot $V$ against $I$:

$V$ (V)	$I$ (A)
2.0	0.20
4.0	0.41
6.0	0.59
8.0	0.80
10.0	1.01

A straight line through the origin means proportional. Its slope is the resistance:

$$R=\frac{\Delta V}{\Delta I}\approx \frac{10.0-2.0}{1.01-0.20}\approx 9.9\Omega$$

Use the slope, not one point

Dividing a single pair of readings uses one measurement and all of its error. The slope of a best-fit line uses every point you took. That is a habit worth carrying into every science course you ever take.

It is a model, not a law of nature

Heat a filament and its resistance climbs, and the line bends. Materials that follow $V=IR$ are called ohmic; plenty are not.

Curriculum connection

D2.4

investigate the relationships between electric current, potential difference, and resistance in electrical circuits, and develop a mathematical model to represent the relationships

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D2.5

apply a mathematical model to calculate electric current, potential difference, and resistance in real- world situations

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