physical science

The heating elements of an electric toaster is typically made of nichrome wire
(an alloy of nickel and chromium). As current passes through the wires, the wires heat up, thus toasting the toast. Estimate the overall resistance of a heating element which is 220 cm long and consists of nichrome wire with a diameter of 0.56 mm. The resistivity of nichrome is 110×〖10〗^(-8) Ω⋅m.(show work)

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  1. R = pL/A.

    p = 110*10^-8 Ohm.m = 110*10^-6 ohm.cm.
    L = 220 cm.
    r = 0.056 cm.
    A = pi*r^2 = 3.14*0.056^2 = 9.85*10^-3 cm^2.

    R = (110*10^-6*220)/(9.85*10^-3) = 2.46 Ohms.

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  2. p = 110*10^-8 Ohm.m = 110*10^-6 ohm.cm.
    L = 220 cm.
    r = 0.028 cm.
    A = pi*r^2 = 2.46*10^-3cm^2.

    R = (110*10^-6*220)/(2.46*10^-3) = 9.84Ohms.

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