A kitchen toaster is designed to draw 6.0 A from a 120 V mains outlet. The heating element consists of a single straight length of nichrome wire of resistivity 1.10×10−6Ωm bent into coils but electrically still one continuous conductor. The total straight-line length of the wire, if it were pulled taut, is 0.80 m.
(a) Determine the resistance the heating element must possess while operating at its rated current and voltage.
(b) From the required resistance, calculate the numerical value of the cross-sectional area the nichrome wire must have.
(c) Hence find the required diameter of the nichrome wire. Give your answer in millimeters.
(d) Suppose the manufacturer accidentally produces wire whose diameter is 10 % smaller than the value found in part (c). Qualitatively discuss how this error would affect (i) the operating current and (ii) the thermal power output of the toaster. No additional arithmetic is required, but support each prediction with clear physical reasoning.