A power supply is connected to two bare wires that are inserted into a glass of salt water. The resistance of the water decreases as the voltage is increased. Sketch a graph of the voltage versus the current in the water showing this type of behavior.

Understanding the connection between voltage (V) and current (I) is fundamental to experiments involving electricity, like the one involving saltwater. This relationship is traditionally described by Ohm's Law, which states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant. The equation is given by
\[\begin{equation} V = IR \end{equation}\], where is the resistance of the conductor.

Implications in an Experimental Setting

In the context of the experiment with the saltwater solution, it is essential to note that this relationship can vary. Normally, one would expect that if you increase the voltage, the current would increase linearly if the resistance stayed the same. However, in a saltwater solution, the resistance changes with voltage, affecting how much current will flow through the solution at different voltages. This results in a non-linear graph, which is differently shaped from a straight line one might expect with a constant resistance.

Resistance is a measure of how much a material opposes the flow of electric current. In the case of the saltwater experiment, the resistance is not a fixed value; it varies with the applied voltage. This is likely due to the dissociation of salt molecules into ions, which increases with the voltage, thereby increasing the number of charge carriers in the solution.

Dynamic Nature of Resistance

As voltage increases, more salt molecules split into charged particles, decreasing the overall resistance of the solution. This decrease in resistance with an increase in voltage is unique as most materials have a resistance that either stays constant or increases slightly due to heating as the current passes through them. Exploring this dynamic relationship provides insight into electrolyte behavior and electrochemical processes, which are fundamental concepts in both chemistry and physics.

Non-linear graphs are curves that depict relationships between variables that do not follow a direct proportionality. In our exercise, we would expect a typical Ohm's Law to produce a straight line graph; however, due to the changing resistance in the saltwater solution as a function of voltage, we obtain a non-linear graph.

Understanding the Curve

The curve's initial shallow slope indicates that at lower voltages, the current increases only slightly with an increase in voltage. As voltage continues to rise, the rate at which the current increases becomes more pronounced reflecting the decreasing resistance. This type of graph is crucial for visualizing complex relationships where variables do not affect one another in a simple, linear way. It provides a more accurate representation of the behavior under study, offering deeper insights into the physics of the medium – in this case, an aqueous salt solution.