Question

students used an ammeter to record the current through three different resistors as the voltage applied to each resistor was increased. the data are shown in the graph below. based on the data, and on the relationship shown in the graphical model, which claim is best about the resistance values of the three resistors?
resistor 1 has the largest resistance because it has the smallest current at each applied voltage.
resistor 3 has the largest resistance because it has the largest current at each applied voltage.
resistor 3 has the largest resistance because it has the smallest current at each applied voltage.
resistor 1 has the largest resistance because it has the largest current at each applied voltage.

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is \(I=\frac{V}{R}\), which can be rearranged to \(R = \frac{V}{I}\).

Step2: Analyze the relationship between \(R\), \(V\), and \(I\)

For a given voltage \(V\), if the current \(I\) is small, the resistance \(R\) is large. Looking at the graph, for each applied voltage (the same \(V\) value across resistors for a particular \(x -\)axis value), Resistor 1 has the smallest current values (lowest \(y -\)axis values among the three resistors). Using \(R=\frac{V}{I}\), when \(V\) is non - zero and \(I\) is small, \(R\) is large. So Resistor 1 has the largest resistance.

Answer:

B. Resistor 1 has the largest resistance because it has the smallest current at each applied voltage.