Question

students used an ammeter to record the currents through three different resistors as the voltage applied to each resistor was increased. the data collected is shown in the model given. based on the graphical evidence 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 2 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 \(V\), resistance \(R\) is inversely proportional to current \(I\). That is, when \(V\) is constant, \(R\propto\frac{1}{I}\).

Step3: Compare the currents of the resistors

Looking at the graph, for each value of applied voltage \(V\), Resistor 1 has the smallest current \(I\). Using \(R=\frac{V}{I}\), with \(V\) non - zero, a smaller \(I\) (for the same \(V\)) means a larger \(R\). So Resistor 1 has the largest resistance.

Answer:

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