problems_section_9[1] - Problems – Electrical Properties...

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Problems – Electrical Properties 1. When subjected to an applied voltage of 10 V, a current of 5 A flows through a metal wire which is 20 m long and 1 mm in diameter. What is the electrical resistivity of the metal. 2. The electrical conductivity of copper is 5.8x10 7 ( W -m) -1 . Determine the resistance of a copper wire which is 1 km long and 0.318 mm in diameter. 3. 12 gauge copper wire is typically used in household electrical wiring. The diameter of this wire is 0.0808 inches. Determine the room-temperature resistance associated with a 12 gauge copper wire 1000 feet long. 4. A pure aluminum interconnect with a semicircular cross-section runs between two transistors on an integrated circuit. The interconnect is 10 microns long and has a radius of 200 nm. Across its length is a voltage of 5 V. The room-temperature conductivity of pure Al is 3.4 x10 7 ( W m) -1 . (a) Determine the current density flowing through the interconnect. (b) The operating temperature of the device is 60 o C. Would you expect the current density flowing through the interconnect to be higher, lower, or the same as that at room temperature? Briefly justify your answer. (c) Suppose an Al - 5 wt% Cu alloy was used in place of pure aluminum. Would you expect the current density flowing through the interconnect to be higher, lower, or the same as that for a pure Al interconnect? Briefly justify your answer. 5. A resistive heating element is to be built from tungsten wire 0.05 mm in diameter. The element should dissipate 50 Watts of power. The resitivity of tungsten is 9 mW -cm. (a) Estimate the length of the wire required for such a device operating at 110 V. (b) Suppose the temperature dependence of the resistivity is included in the calculation. Would the design now call for a longer or shorter wire relative to when the T-dependence was ignored? (c) What, if any, effect would a nick in the wire have on its performance? 6. One important application of metal conductors is for wire in resistance-heated furnace elements. Consider a 1 mm diameter chromel (a Ni-Cr alloy) to produce a 1 kW furnace coil in a furnace operated at 110 V. (a) What length of wire would be required for this furnace design? The resistivity of chromel is 1.08x10 -6 W -m at room temperature.
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(b) When in use as a heating element the temperature of the wire increases, and the resistivity of the chromel changes. How would you expect this change to affect the length of the wire you specify? Briefly justify your answer. (c) Suppose the wire is deformed prior to installation so it has a high concentration of defects such as dislocations and grain boundaries. How would this affect the calculation? Would the length need to be longer/shorter when using the high-defect wire. 7. The electrical conductivity of copper-zinc alloys (brasses) as a function of composition and degree of deformation is described in the adjacent figure. Rationalize the decrease in conductivity due to composition and deformation.
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problems_section_9[1] - Problems – Electrical Properties...

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