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The heating element 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 110x10-​ 8​Ω•m.

Respuesta :

Answer:

The resistance of a heating element is 0.9825 ohms.

Explanation:

It is given that,

Length of wire, l = 220 cm = 0.22 m

Diameter of wire is 0.56 mm.

Radius, r = 0.28 mm

Resistivity of nichrome, [tex]\rho=110\times 10^{-8}\ \Omega-m[/tex]

The resistance of a wire in terms of resistivity is given by :

[tex]R=\rho\dfrac{l}{A}[/tex]

[tex]R=110\times 10^{-8}\times \dfrac{0.22}{\pi \times (0.28\times 10^{-3})^2}\\\\R=0.982\ \Omega[/tex]

So, resistance of a heating element is 0.9825 ohms.

The resistance of a heating element is 0.9825 Ω.

Given that the length of wire l = 220 cm = 0.22 m ,

diameter d = 0.56 mm. ⇒ radius r = 0.28 mm

Resistivity of nichrome, ρ =  [tex]110*10^{8}[/tex] Ωm

The resistance R is given by :

R = ρl/A

  [tex]=110*10^{8}*0.22/3.14*(2.8*10^{-4}) ^{2}[/tex]

R = 0.9825 Ω is the resistance of a heating element.

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