Question

21 use the information and graph to answer the following question. while investigating the relationship between voltage, current, and resistance, students connected different batteries to different circuits and recorded measurements of battery voltage and current flowing through the battery. the students results are shown on the graph. circuit current vs. battery voltage which claim can be made about the resistance of the circuit? a the resistance of the circuits increased as battery voltage increased. b the resistance of the circuits decreased as battery voltage increased. c the resistance of the circuits remained constant as the battery voltage increased. d the resistance of the circuits could have either increased or decreased as the battery voltage increased.

Explanation:

Step1: Recall Ohm's Law

Ohm's Law is \(V = IR\), where \(V\) is voltage, \(I\) is current, and \(R\) is resistance. Rearranging for \(R\) gives \(R=\frac{V}{I}\).

Step2: Analyze the graph

The graph is a straight - line graph of \(I\) (current) vs \(V\) (voltage). The slope of a \(I - V\) graph is \(\frac{I}{V}=\frac{1}{R}\). Since the graph is a straight line, the slope is constant. If \(\frac{I}{V}\) is constant, then \(R=\frac{V}{I}\) is also constant.

Answer:

C. The resistance of the circuits remained constant as the battery voltage increased.