A 500- W heating coil designed to operate from 110 V is made of Nichrome wire 0.500 mm in diamet

A 500- W heating coil designed to operate from 110 V is made...

Key Concepts

Resistivity

Resistivity is an intrinsic property of a material that quantifies how strongly it opposes electrical conduction. It is dependent on the material's composition and structure and is used in calculating the resistance of a conductor. In practical applications, knowing the resistivity helps determine the dimensions and length of a conductor needed to achieve a particular resistance.

Electrical Resistance

Electrical resistance is a measure of how strongly a material opposes the flow of electric current. It is determined by the material's resistivity, its length, and its cross?sectional area, as described by the relation R = (?L)/A. This concept is fundamental in circuits and helps in designing components like heating elements, where a specific resistance is required to achieve desired performance under a given voltage.

Temperature Dependence of Resistivity

The resistivity of materials, especially metals, typically changes with temperature. As temperature increases, the lattice vibrations in the material also increase, which generally causes an increase in resistivity. This temperature dependence is critical when designing devices like heating coils because the operating temperature can significantly alter the performance or power output from the expected value at room temperature.

Electrical Power Dissipation

Electrical power dissipation in a resistive element occurs when electric energy is converted into heat as current flows through the resistor. It is calculated using formulas such as P = V^2/R or P = I^2R. Understanding power dissipation is essential for ensuring that components like heating elements deliver the intended energy output while operating within safe and efficient limits.

Wire Geometry

Wire geometry, particularly the cross-sectional area and length of the wire, plays a crucial role in determining its resistance. The cross-sectional area, which is related to the diameter for cylindrical wires, influences how much current can pass through. Accurate calculations of a wire's geometry are necessary when designing electrical components to ensure they meet the desired electrical and thermal specifications.

Transcript

00:01 In this problem we are given the power of filament is equal to 500 watt and the potential difference is equal to 110 volts and the diameter is equal to 0 .5 millimeter which can be written as 5 multiply by tank power minus 4 meter.

00:25 Then radius will be equal to half of diameter which is equal to 2 .5 multiply by tank power minus 2 meter and the initial temperature t1 is 20 degrees centigrade and the final temperature is 1200 degrees centigrade thus the changing temperature will be equal to 1180 degree centigrade in the first part you have to find the length so for that first of all you know that power is equal to permission difference squared divided by r which is equal to 500 watt is here pressure difference is equal to 110 volt square divided by r will be equal to 500 watt when we solve this for r we get resistance is equal to 24 .2 oam now as we know that resistance is equal to sensitivity into length divided by area if we want to find the length and we will when we rearrange this equation for length we get length is equal to resistivity into area divided by sorry resistance into area divided by resistivity as here resistance is r area is pi r square divided by restivity we will substitute the values in this equation when r is equal to area is pi 3 .14 r square is 2 .5 multiply by tank power minus 4 meter square into restace is 24 .2 oham divided by resistuity is equal to 1 .50 cross tankie power minus 6 oam meter when we solve for this we get note or rather l we are solving this for l we get l is equal to 3 .16 meter which is the answer of the first part of the question now in the second part part b of the question we will find the power before that we find resistance at 1200 disintegrate which can be found by using formula r is equal to r node into 1 plus alpha delta t r will be equal to r node is 24 .2 oam into 1 plus temperature coefficient of rest 2 t is equal to 0 .4 multiplied by tanker power minus 3 oam meter and delta t is 1180 degrees centigrade so when we solve for r we get r is equal to 35 .6 oom a 1200 degrees centigrade now we will find power a 1200 degrees integrate will be equal to delta v square divided by r as delta v is equal to delta v is equal to the ratio difference is equal to 110 volts squared by raise test is 35 .6...

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