Example from Physics, 19.1 Ohm's law

Determine Resistance from Current-Voltage Graph

Suppose you apply several different voltages across a circuit and measure the current that runs through the circuit. A plot of your results is shown in Figure 19.7. What is the resistance of the circuit?

The graph shows current in milliamperes on the y-axis and voltage in volts on the x-axis with a straight line such that at 3V, the current is 3 mA.

Figure 19.7 The line shows the current as a function of voltage. Notice that the current is given in milliamperes. For example, at 3 V, the current is 0.003 A, or 3 mA.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The plot shows that current is proportional to voltage, which is Ohm’s law. In Ohm’s law ( $V = I R$ ), the constant of proportionality is the resistance R. Because the graph shows current as a function of voltage, we have to rearrange Ohm’s law in that form: $I = \frac{V}{R} = \frac{1}{R} \times V$ . This shows that the slope of the line of I versus V is $\frac{1}{R}$ . Thus, if we find the slope of the line in Figure 19.7, we can calculate the resistance R.
Solution
The slope of the line is the rise divided by the run. Looking at the lower-left square of the grid, we see that the line rises by 1 mA (0.001 A) and runs over a voltage of 1 V. Thus, the slope of the line is

$slope = \frac{0.001 A}{1 V.}$
19.7

Equating the slope with $\frac{1}{R}$ and solving for R gives

$\begin{matrix} \frac{1}{R} & = & \frac{0.001 A}{1} \\ R & = & \frac{1 V}{0.001 A} = 1,000 Ω \end{matrix}$
19.8

or 1 k-ohm.

0 of 2 steps open

How did it go?

Strategy

Solution

Strategy

Solution