The voltage drop Va b across each of resistors A and B was...

The voltage drop $V_{a b}$ across each of resistors $A$ and $B$ was measured as a function of the current $I$ in the resistor. The results are shown in the table: (a) For each resistor, graph $V_{a b}$ as a function of $I$ and graph the resistance $R=V_{a b} / I$ as a function of $I$. (b) Does resistor $A$ obey Ohm's law? Explain. (c) Does resistor $B$ obey Ohm's law? Explain. (d) What is the power dissipated in $A$ if it is connected to a $4.00 \mathrm{~V}$ battery that has negligible internal resistance? (e) What is the power dissipated in $B$ if it is connected to the battery?

The voltage drop $V_{a b}$ across each of resistors $A$ and $B$ was measured as a function of the current $I$ in the resistor. The results are shown in the table:
(a) For each resistor, graph $V_{a b}$ as a function of $I$ and graph the resistance $R=V_{a b} / I$ as a function of $I$. (b) Does resistor $A$ obey Ohm's law? Explain. (c) Does resistor $B$ obey Ohm's law? Explain.
(d) What is the power dissipated in $A$ if it is connected to a $4.00 \mathrm{~V}$ battery that has negligible internal resistance? (e) What is the power dissipated in $B$ if it is connected to the battery?

Key Concepts

Ohm's Law

Ohm's law is a fundamental principle in electrical circuits, stating that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, with the proportionality constant being the resistance. This concept is used to determine if a resistor behaves ideally, meaning that the resistance remains constant regardless of the applied voltage and current.

Electrical Resistance

Electrical resistance is a measure of a material or component's opposition to the flow of electric current. It is defined as the ratio of the voltage across the component to the current flowing through it. Analyzing resistance helps in understanding whether a component, like a resistor, has a consistent value (ohmic behavior) or if it changes with varying current or voltage (non-ohmic behavior).

Graphical Analysis of Experimental Data

Graphical analysis involves plotting experimental variables, such as voltage and current, to visually interpret their relationships. For electrical components, a linear graph of voltage versus current indicates a constant resistance, while plotting resistance as a function of current can reveal any variations in the component's behavior. This method is key in determining whether a resistor obeys Ohm's law.

Electrical Power Dissipation

Electrical power dissipation in a resistor refers to the process by which electrical energy is converted into heat. It is calculated using formulas like P = V²/R or P = I²R. Understanding power dissipation is essential for ensuring that components do not exceed their thermal limits and for designing circuits that are both efficient and safe.