Household wiring has sometimes used aluminium instead of copper. What would be the resistance of the same wire if it were made of aluminum?

Small changes in the length of an object can be measured using a strain gauge sensor, which is a wire that when undeformed has length ℓ₀, cross-sectional area A₀, and resistance R₀. This sensor is rigidly affixed to the object’s surface, aligning its length in the direction in which length changes are to be measured. As the object deforms, the length of the wire sensor changes by Δℓ, and the resulting change ΔR in the sensor’s resistance is measured. Assuming that as the solid wire is deformed to a length ℓ, its density and volume remain constant (only approximately valid), show that the strain ( = Δℓ / ℓ₀ ) of the wire sensor, and thus of the object to which it is attached, is approximately ΔR / 2R₀.

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).

Household wiring has sometimes used aluminium instead of copper.Typical copper wire used for home wiring in the U.S. has a diameter of 1.63 mm. What is the resistance of 125 m of this wire?

Estimate how far can an average electron move along one of the connecting wires of a 750-W toaster during an alternating current cycle? The power cord has copper wires of diameter 1.7 mm and is plugged into a 60-Hz 120-V ac outlet. [Hint: For sinusoidal motion, Chapter 14, we saw that the maximum distance traveled from equilibrium (amplitude A) is proportional to the maximum (drift) speed (Eq. 14–9a). This maximum drift speed is related to the maximum current (Section 25–8), which is calculated as the first step here; see Chapter 14.]

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?