Question

# A toaster rated at 1050 W operates on a 120V household circuitand a 4.00 m length of a nichrome wire as its heatingelement. The operating temperature of this element is 320degrees celsius. What is the cross-sectional area of the wire?

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A toaster rated at 1050 W operates on a 120V household circuitand a 4.00 m length of a nichrome wire as its heatingelement. The operating temperature of this element is 320degrees celsius.
What is the cross-sectional area of the wire?

2021-05-18

$$\displaystyle{P}=\frac{{V}^{{{2}}}}{{R}}$$
$$\displaystyle{R}=\rho\frac{{L}}{{A}}$$
$$\displaystyle\rho=\rho_{{{0}}}{\left[{1}+\alpha{\left({T}-{T}_{{{0}}}\right)}\right]}$$
$$\displaystyle{A}={\frac{{\rho{L}}}{{{R}}}}={\frac{{\rho{L}{P}}}{{{V}^{{{2}}}}}}={\frac{{\rho_{{{0}}}{L}{P}{\left[{1}+\alpha{\left({T}-{T}_{{{0}}}\right)}\right]}}}{{{V}^{{{2}}}}}}$$
The book I have gives for nichrome:
$$\displaystyle\rho_{{{0}}}={1}\times{10}^{{-{6}}}\rho-{m}{T}_{{{0}}}={20}{C}$$
$$\displaystyle\alpha={0.0004}{C}^{{-{1}}}$$