# 9.6 Superconductors  (Page 5/11)

 Page 5 / 11

## Conceptual questions

What requirement for superconductivity makes current superconducting devices expensive to operate?

Very low temperatures necessitate refrigeration. Some materials require liquid nitrogen to cool them below their critical temperatures. Other materials may need liquid helium, which is even more costly.

Name two applications for superconductivity listed in this section and explain how superconductivity is used in the application. Can you think of a use for superconductivity that is not listed?

## Problems

Consider a power plant is located 60 km away from a residential area uses 0-gauge $\left(A=42.40\phantom{\rule{0.2em}{0ex}}{\text{mm}}^{2}\right)$ wire of copper to transmit power at a current of $I=100.00\phantom{\rule{0.2em}{0ex}}\text{A}$ . How much more power is dissipated in the copper wires than it would be in superconducting wires?

$\begin{array}{}\\ \\ \\ \\ {R}_{\text{copper}}=0.24\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}\hfill \\ P=2.377\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\text{W}\hfill \end{array}$

A wire is drawn through a die, stretching it to four times its original length. By what factor does its resistance increase?

Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has $\alpha =-0.06\text{/}\text{°}\text{C}$ ) when it is at the same temperature as the patient. What is a patient’s temperature if the thermistor’s resistance at that temperature is 82.0% of its value at $37\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ (normal body temperature)?

$\begin{array}{c}R={R}_{0}\left(1+\alpha \left(T-{T}_{0}\right)\right)\hfill \\ 0.82{R}_{0}={R}_{0}\left(1+\alpha \left(T-{T}_{0}\right)\right),\phantom{\rule{0.8em}{0ex}}0.82=1-0.06\left(T-37\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\right),\phantom{\rule{0.8em}{0ex}}T=40\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\hfill \end{array}$

Electrical power generators are sometimes “load tested” by passing current through a large vat of water. A similar method can be used to test the heat output of a resistor. A $R=30\phantom{\rule{0.2em}{0ex}}\text{Ω}$ resistor is connected to a 9.0-V battery and the resistor leads are waterproofed and the resistor is placed in 1.0 kg of room temperature water $\left(T=20\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\right)$ . Current runs through the resistor for 20 minutes. Assuming all the electrical energy dissipated by the resistor is converted to heat, what is the final temperature of the water?

A 12-guage gold wire has a length of 1 meter. (a) What would be the length of a silver 12-gauge wire with the same resistance? (b) What are their respective resistances at the temperature of boiling water?

a. ${R}_{\text{Au}}={R}_{\text{Ag}},\phantom{\rule{0.8em}{0ex}}{\rho }_{\text{Au}}\frac{{L}_{\text{Au}}}{{A}_{\text{Au}}}={\rho }_{\text{Ag}}\frac{{L}_{\text{Ag}}}{{A}_{\text{Ag}}},\phantom{\rule{0.8em}{0ex}}{L}_{\text{Ag}}=1.53\phantom{\rule{0.2em}{0ex}}\text{m}$ ;
b. ${R}_{\text{Au,20 °C}}=0.0074\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.8em}{0ex}}{R}_{\text{Au,100 °C}}=0.0094\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}},\phantom{\rule{0.8em}{0ex}}{R}_{\text{Ag},100\phantom{\rule{0.2em}{0ex}}\text{°C}}=0.0096\phantom{\rule{0.2em}{0ex}}\text{Ω}$

What is the change in temperature required to decrease the resistance for a carbon resistor by 10%?

## Additional problems

A coaxial cable consists of an inner conductor with radius ${r}_{\text{i}}=0.25\phantom{\rule{0.2em}{0ex}}\text{cm}$ and an outer radius of ${r}_{\text{o}}=0.5\phantom{\rule{0.2em}{0ex}}\text{cm}$ and has a length of 10 meters. Plastic, with a resistivity of $\rho =2.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{13}\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}·\text{m}$ , separates the two conductors. What is the resistance of the cable?

$\begin{array}{ccc}\hfill dR& =\hfill & \frac{\rho }{2\pi rL}dr\hfill \\ \hfill R& =\hfill & \frac{\rho }{2\pi L}\text{ln}\phantom{\rule{0.2em}{0ex}}\frac{{r}_{\text{o}}}{{r}_{\text{i}}}\hfill \\ \hfill R& =\hfill & 2.21\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{11}\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}\hfill \end{array}$

A 10.00-meter long wire cable that is made of copper has a resistance of 0.051 ohms. (a) What is the weight if the wire was made of copper? (b) What is the weight of a 10.00-meter-long wire of the same gauge made of aluminum? (c)What is the resistance of the aluminum wire? The density of copper is $8960{\phantom{\rule{0.2em}{0ex}}\text{kg/m}}^{3}$ and the density of aluminum is $2760{\phantom{\rule{0.2em}{0ex}}\text{kg/m}}^{3}$ .

A nichrome rod that is 3.00 mm long with a cross-sectional area of $1.00{\phantom{\rule{0.2em}{0ex}}\text{mm}}^{2}$ is used for a digital thermometer. (a) What is the resistance at room temperature? (b) What is the resistance at body temperature?

a.
${R}_{0}=3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{Ω}$ ; b.
$\begin{array}{ccc}\hfill {T}_{\text{c}}& =\hfill & 37.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\hfill \\ \hfill R& =\hfill & 3.02\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}\hfill \end{array}$

#### Questions & Answers

what is the difference between temperature and heat
Ishom Reply
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Abdul
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
Gamma
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
TONEJIT Reply
A charge insulator can be discharged by passing it just above a flame. Explain.
Mudassar Reply
of the three vectors in the equation F=qv×b which pairs are always at right angles?
DRASHTI Reply
what is an ideal gas?
Justine Reply
What is meant by zero Kelvin ?
Justine
Why does water cool when put in the pot ?
Justine
when we pour the water in a vessel(pot) the hot body(water) loses its heat to the surrounding in order to maintain thermal equilibrium.Thus,water cools.
rupendra
when we drop water in the pot, the pot body loses heat to surrounded in order to maintain thermal equilibrium thus,water cool.
Srabon
types of thermometer?
yemisi Reply
thermometer, Radiation thermometer and vapour pressure thermometer.liquid thermometer use thermometric liquid like mercury ,alcohol etc.
rupendra
liqid thermometer ,gas thermometer, resitance thermometer,thermo electric thermometer , radiation thermometer andvapour pressure thermometer
rupendra
calculate the quantity of heat required to rise the temperature of 1gmail of ice _10 to 110
Dargu Reply
A 40cm tall glass is filled with water to a depth of 30cm. A.what is the gauge pressure at the bottom of the glass? B.what is the absolute pressure at the bottom of the glass?
Abdulaziz Reply
A glass bottle full of mercury has mass 50g when heated through 35degree, 2.43g of mercury was expelled. Calculate the mass of the mercury remaining in the bottle
Anjorin Reply
Two electric point charges Q=2micro coulomb are fixed in space a distance 2.0cm apart. calculate the electric potential at the point p located a distance d/2 above the central point between two charges
Abdul Reply
what is wave
Ahmed Reply
A wave is a periodic disturbance which travel with a finite velocity and remains unchanged in type as it travels.
Justine
What's a wave motion?
Justine
What is charge bodies
Oje Reply
which have free elections
Usman
Show that if a vector is gradient of a scaler function then its line around a closed path is zero
Pak
Charge bodies are those which have free electons
Pak
the melting point of gold is 1064degree cencius and is boiling point is 2660 degree cenciu
Ilyas Reply
is Thomas's young experiment interference experiment or diffraction experiment or both
Ilyas Reply
An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?
eugene
A 4.0kg mess kit sliding on a fractionless surface explodes into two 2.0 kg parts.3.0 m/s due to north and 0.5 m/s 30 degree north of east. what is the speed of the mess kit
Shahid
it's a line used to represent a complex electrical quantity as a vector
Gift Reply

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