The level of liquid helium (temperature ≈ 4 K) 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 difference V across this wire. Since the superconducting critical temperature for NbTi is 10 K, 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 f = x/l to be the fraction of the tank filled with liquid helium (Fig. 18–38) and V₀ to be the value of V when the tank is empty (f = 0). Determine the relation between f and V (in terms of V₀).

Constant / Helium vapor (>10K) Liquid helium (4 K) FIGURE 18-38 Nomal Superconducting