A current-carrying gold wire has diameter 0.87 mm. The electric field in the wire is 0.54 V /

step 1 We have a gold wire that has a diameter of 0 .87 millimeters. We're going to convert this to rad

A current-carrying gold wire has diameter 0.87 mm. The...

A current-carrying gold wire has diameter $0.87 \mathrm{~mm}$. The electric field in the wire is $0.54 \mathrm{~V} / \mathrm{m}$. What are (a) the current carried by the wire; (b) the potential difference between two points in the wire $7.0 \mathrm{~m}$ apart; (c) the resistance of a $7.0 \mathrm{~m}$ length of this wire?

A current-carrying gold wire has diameter $0.87 \mathrm{~mm}$. The electric field in the wire is $0.54 \mathrm{~V} / \mathrm{m}$. What are (a) the current carried by the wire;
(b) the potential difference between two points in the wire $7.0 \mathrm{~m}$ apart;
(c) the resistance of a $7.0 \mathrm{~m}$ length of this wire?

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle that relates the voltage (potential difference), current, and resistance in an electrical circuit. It is expressed as V = IR, where V is the voltage, I is the current, and R is the resistance. This law is essential for understanding how electrical circuits behave and for calculating any one of the quantities if the other two are known.

Electric Field and Potential Difference

The electric field in a conductor is related to the potential difference across a distance by the equation V = E × L, where E is the electric field and L is the length over which the field is applied. This relationship is crucial for understanding how a voltage gradient drives current through a material, particularly when analyzing experimental setups involving extended portions of conductors.

Resistance of a Conductor and Resistivity

The resistance of a uniform conductor depends on its material properties and its geometry. It is given by the formula R = ?L/A, where ? is the material's resistivity, L is the length of the conductor, and A is its cross-sectional area. This concept explains how the ease of charge flow (or resistance to it) is influenced by both the inherent property of the material and its physical dimensions.

Geometric Factors in Electrical Conduction

The cross-sectional area of a conductor plays a key role in determining its resistance and the current it can carry. A larger area allows for more charge carriers to pass through simultaneously, reducing resistance and increasing current capacity. The area is typically calculated using the formula A = ?r² for circular wires, where r is the radius of the wire, linking geometric factors directly to electrical behavior.

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