A coil of Nichrome wire is 25.0 m long. The wire has a diameter of 0.400 mm and is at 20.0^∘ C .

step 1 As we know that area A is equal to pi d square by 4. So I am putting the value of D here. So on

A coil of Nichrome wire is 25.0 m long. The wire has a...

A coil of Nichrome wire is $25.0 \mathrm{m}$ long. The wire has a diameter of $0.400 \mathrm{mm}$ and is at $20.0^{\circ} \mathrm{C} .$ If it carries a current of $0.500 \mathrm{A},$ what are (a) the magnitude of the clectric field in the wire, and (b) the power delivered to it? (c) What If? If the temperature is increased to $340^{\circ} \mathrm{C}$ and the voltage across the wire remains constant, what is the power delivered?

A coil of Nichrome wire is $25.0 \mathrm{m}$ long. The wire has a diameter of $0.400 \mathrm{mm}$ and is at $20.0^{\circ} \mathrm{C} .$ If it carries a current of $0.500 \mathrm{A},$ what are (a) the magnitude of the clectric field in the wire, and (b) the power delivered to it?
(c) What If? If the temperature is increased to $340^{\circ} \mathrm{C}$ and the voltage across the wire remains constant, what is the power delivered?

Key Concepts

Electric Field in a Conductor

This concept involves understanding that within a uniform conductor under a constant voltage, the electric field is uniform and given by the voltage difference divided by the length of the conductor. It explains how the potential gradient drives the flow of charge, which is fundamental in analyzing current flow in materials.

Resistivity and Resistance Calculation

Resistance of a material is determined by its intrinsic resistivity along with its geometric dimensions, specifically its length and cross-sectional area. The relationship R = ?(L/A) is crucial in evaluating how much a given material opposes the flow of electric current, regardless of the actual material used, while abstracting away example-specific numbers.

Power Dissipation in Resistive Elements

Power dissipation in a resistor, which converts electrical energy into heat, is governed by equations such as P = I²R and P = V²/R. These formulas are central in analyzing and designing circuits, ensuring that components operate safely within their power ratings.

Temperature Dependence of Resistivity

Many conductive materials exhibit changes in resistivity with temperature, typically increasing as temperature rises. This concept is essential because an increase in temperature can lead to a higher resistance, which in turn affects the current and power dissipation when other parameters, such as the applied voltage, are held constant.

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