Question

The heating element of a hairdryer is made of coiled nichrome wire. The diameter of the wire is 0.46 mm and the length of the wire is 7.3 m. Calculate the resistance of the element at 0 degree Celsius. The resistivity of the nichrome is 110 x 10^-6 ohms per meter

Answer 1

Answer on Question #69949-Physics-Other

The heating element of a hairdryer is made of coiled nichrome wire. The diameter of the wire is 0.46 mm and the length of the wire is 7.3 m. Calculate the resistance of the element at 0 degree Celsius. The resistivity of the nichrome is $110 \times 10^{-6}$ ohms per meter

Solution

The crosssectional area is given by the formula:

$$A = \frac {\pi d ^ {2}}{4}$$

The resistance of the element is

$$R = \rho \frac {l}{A} = \rho \frac {l}{\frac {\pi d ^ {2}}{4}}.$$ $$R = 4 \cdot 110 \cdot 10^{-6} \frac {7.3}{\pi (0.46 \cdot 10^{-3})^2} = 4.8 \, \text{k}\Omega.$$

Answer: $4.8 \, \text{k}\Omega$

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