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.]

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.