In order to double its resistance, by how much would you have to increase the temperature of a piece of the following? (a) copper (The temperature coefficient of resistance for copper is 3.9 × 10-3 (°C)-¹.) °C (b) Nichrome (The temperature coefficient of resistance for Nichrome is 4.0 × 10-4 (°C)-¹.) °℃

In order to double its resistance, by how much would you have to increase the temperature of a piece of the following? (a) copper (The temperature coefficient of resistance for copper is 3.9 × 10-3 (°C)-¹.) °C (b) Nichrome (The temperature coefficient of resistance for Nichrome is 4.0 × 10-4 (°C)-¹.) °℃

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter27: Current And Resistance

Section: Chapter Questions

Problem 27.73AP

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Review. When a straight wire is warmed, its resistance is given by R = R0,[1 + a(T T0)] according to Equation 27.20, where a is the temperature coefficient of resistivity. This expression needs to be modified if we include the change in dimensions of the wire due to thermal expansion. For a copper wire of radius 0.100 0 mm and length 2.000 m, find its resistance at 100.0C, including the effects of both thermal expansion and temperature variation of resistivity. Assume the coefficients are known to four significant figures.
When a straight wire is heated, its resistance changes according to the equation R = R0 [1 + (T T0)] (Eq. 17.7), where is the temperature coefficient of resistivity. (a) Show that a more precise result, which includes the length and area of a wire change when it is heated, is R=R0[1+(TT0)][1+(TT0)][1+2(TT0)] where is the coefficient of linear expansion. (See Topic 10.) (b) Compare the two results for a 2.00-m-long copper wire of radius 0.100 mm, starting at 20.0C and heated to 100.0C.
Use the atomic theory of matter to explain why the resistance of a material should increase as its temperature increases.
When a straight wire is heated, its resistance changes according to the equation R = R0 [1 + (T T0)] (Eq. 17.7), where is the temperature coefficient of resistivity. (a) Show that a more precise result, which includes the length and area of a wire change when it is heated, is R=R0[1+(TT0)][1+(TT0)][1+2(TT0)] where is the coefficient of linear expansion. (See Topic 10.) (b) Compare the two results for a 2.00-m-long copper wire of radius 0.100 mm, starting at 20.0C and heated to 100.0C.
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Explain why R=R0(1 + a?T) for the temperature variation of the resistance R of an object is not as accurate as P=P0(1 + a?T) which gives the temperature variation of resistivity P.
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Power P0 = I0 V0 is delivered to a resistor of resistance R0. If the resistance is doubled (Rnew = 2R0) while the voltage is adjusted such that the current is constant, what are the ratios (a) Pnew/P0 and (b) Vnew/V0? If, instead, the resistance is held constant while Pnew = 2P0, what are the ratios (c) Vnew/V0, and (d) Inew/I0?
Power P0 = I0 V0 is delivered to a resistor of resistance R0. If the resistance is doubled (Rnew = 2R0) while the voltage is adjusted such that the current is constant, what are the ratios (a) Pnew/P0 and (b) Vnew/V0? If, instead, the resistance is held constant while Pnew = 2P0, what are the ratios (c) Vnew/V0, and (d) Inew/I0?
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