A 1.50 m cylindrical rod of diameter 0.500 cm is connected to a power supply that maintains a

step 1 We have a rod that has a length of 1 .5 meters. It has a diameter of 0 .5 centimeters, but we wa

A 1.50 m cylindrical rod of diameter 0.500 cm is connected...

A $1.50 \mathrm{~m}$ cylindrical rod of diameter $0.500 \mathrm{~cm}$ is connected to a power supply that maintains a constant potential difference of $17.0 \mathrm{~V}$ across its ends, while an ammeter measures the current through it. You observe that at room temperature $\left(20.0^{\circ} \mathrm{C}\right)$ the ammeter reads $18.8 \mathrm{~A}$, while at $92.0^{\circ} \mathrm{C}$ it reads $17.1 \mathrm{~A}$. You can ignore any thermal expansion of the rod. Find (a) the resistivity at $20.0^{\circ} \mathrm{C}$ and $(\mathrm{b})$ the temperature coefficient of resistivity at $20^{\circ} \mathrm{C}$ for the material of the rod.

Key Concepts

Ohm's Law

Ohm's law relates voltage, current, and resistance in an electrical circuit by the formula V = IR. It is essential for determining the resistance of a conductor when the voltage across it and the current flowing through it are known.

Resistivity and Its Relation to Resistance

Resistivity is a material-specific property that characterizes how strongly the material opposes the flow of electric current. The resistance of a conductor is given by the formula R = ?L/A, where L is the length and A is the cross-sectional area. This relationship is fundamental for connecting material properties with measurable electrical characteristics.

Geometric Considerations in Conductivity

The dimensions of a conductor, particularly its length and cross-sectional area, play a crucial role in determining its resistance. For a cylindrical rod, the cross-sectional area is calculated using the diameter, and this geometric factor is key when relating measured resistance to the material's resistivity.

Temperature Coefficient of Resistivity

The temperature coefficient of resistivity quantifies the rate at which a material's resistivity changes with temperature. It is defined by the change in resistivity per degree change in temperature, relative to the resistivity at a reference temperature, and is essential for understanding how electrical properties vary with thermal conditions.

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