Explanation:
Given:
Solving for 
:
where:
Integrating to get 
with initial conditions 
:
Integrating to get x with initial conditions x(0) = 0:
When t=T:
D, Metamorphism
-Metamorphic rocks are any rocks that change into another rock when subjected to high heat and pressure.
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English "natural philosopher" (the contemporary term for physicist) Michael Faraday is renowned for his discovery of the principles of electro-magnetic induction and electro-magnetic rotation, the interaction between electricity and magnetism that led to the development of the electric motor and generator. The unit of measurement of electrical capacitance - the farad (F) - is named in his honor.
Faraday's experimental work in chemistry, which included the discovery of benzene, also led him to the first documented observation of a material that we now call a semiconductor. While investigating the effect of temperature on "sulphurette of silver" (silver sulfide) in 1833 he found that electrical conductivity increased with increasing temperature. This effect, typical of semiconductors, is the opposite of that measured in metals such as copper, where conductivity decreases as temperature is increased.
In a chapter entitled "On Conducting Power Generally" in his book Experimental Researches in Electricity Faraday writes "I have lately met with an extraordinary case ... which is in direct contrast with the influence of heat upon metallic bodies ... On applying a lamp ... the conducting power rose rapidly with the heat ... On removing the lamp and allowing the heat to fall, the effects were reversed."
We now understand that raising the temperature of most semiconductors increases the density of charge carriers inside them and hence their conductivity. This effect is used to make thermistors - special resistors that exhibit a decrease in electrical resistance (or an increase in conductivity) with an increase in temperature.
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Next Milestone
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Contemporary Documents
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<span>Faraday, M. Experimental Researches in Electricity, Volume 1. (London: Richard and John Edward Taylor, 1839) pp.122-124 (para. 432). Note: This section appears on different pages in later editions of the book. The material in the book is reprinted from articles by Faraday published in the Philosophical Transactions of the Royal Society of 1831-1838. </span>
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More Information
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<span>Hirshfeld, Alan W. The Electric Life of Michael Faraday. Walker & Company (March 7, 2006).</span>
<span>Friedel, Robert D. Lines and Waves: Faraday, Maxwell and 150 Years of Electromagnetism. Center for the History of Electrical Engineering, Institute of Electrical and Electronics Engineers (1981).</span>
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