Figure 26.27 gives the electric potential V(x) along a cop-...

Figure 26.27 gives the electric potential $V(x)$ along a cop- per wire carrying uniform current from a point of higher potential $V_{s}=12.0 \mu \mathrm{V}$ at $x=0$ to a point of zero potential at $x_{s}=3.00 \mathrm{m} .$ The wire has a radius of 2.00 $\mathrm{mm} .$ What is the current in the wire?

Figure 26.27 gives the electric potential $V(x)$ along a cop-
per wire carrying uniform current
from a point of higher potential $V_{s}=12.0 \mu \mathrm{V}$ at $x=0$ to a point of
zero potential at $x_{s}=3.00 \mathrm{m} .$ The
wire has a radius of 2.00 $\mathrm{mm} .$ What
is the current in the wire?

Key Concepts

Cross-Sectional Area Calculation

The cross-sectional area of a conductor, particularly when it has a circular cross-section, is essential for determining its resistance. The area is calculated using the formula A = ?r², where r is the radius of the wire. This calculation converts physical dimensions into electrical parameters.

Uniform Current Flow

In problems involving a long, uniform conductor, it is typically assumed that the current flows uniformly throughout its cross-section. This assumption simplifies the calculations and validates the use of the resistance formula derived from the material's geometry and intrinsic properties.

Resistance of a Conductor

The resistance of a conductor is determined by both its material properties and its geometrical dimensions. It is calculated using the formula R = (?L)/A, where ? is the resistivity of the material, L is the length of the conductor, and A is its cross-sectional area. This concept links the physical dimensions of the conductor to its electrical behavior.

Ohm's Law

Ohm's law is the fundamental relationship in electrical circuits that relates the voltage (potential difference) across a conductor to the current flowing through it and the resistance of the conductor. It is expressed as V = IR, where V is the voltage, I is the current, and R is the resistance. This principle is used to calculate one variable when the other two are known.

Electrical Resistivity

Electrical resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. In analyses involving current-carrying conductors, the resistivity of the material (such as copper) is used along with the geometry of the conductor to calculate its resistance.

Transcript

Please give Ace some feedback