The level of liquid helium (temperature ≈ 4K) in its storage tank can be monitored using a vertically aligned niobium–titanium (NbTi) wire, whose length ℓ spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current I at all times in the NbTi wire and a voltmeter monitors the voltage V across this wire. The NbTi wire is superconducting ( R = 0) if below its transition temperature of 10 K, so the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above 10 K) is in the normal state. Define ƒ = x/ℓ to be the fraction of the tank filled with liquid helium (Fig. 25–40) and V₀ to be the value of the voltage V when the tank is empty (ƒ = 0) . Determine the relation between f and V (in terms of V₀).
Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 1250 W of power total. What power is wasted in 25.0 m of this wire?
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Key Concepts
Ohm's Law
Resistance of a Wire
Power Loss in Electrical Circuits
A 100-W, 120-V incandescent lightbulb has a resistance of 12 Ω when cold (20°C) and 150 Ω when on (hot). Calculate its power consumption (a) at the instant it is turned on, and (b) after a few moments when it is hot.
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