Question #314635

Calculate the length of the resistor of a circular wire used in a heater element connected to a 240V supply and the heater consumes 8 joules of energy in 0,25 seconds. The resistor element is made of aluminium and it has a uniform cross-sectional area with a diameter of 0,00016 inches.


Hints: 1inch = 25,4 mm, resistivity of aluminium = 2,825 x 10- 6 cm

1
Expert's answer
2022-03-21T12:45:41-0400

Power

P=EtP=\frac{E}{t}

P=80.25=32WP=\frac{8}{0.25}=32W

P=V2RP=\frac{V^2}{R}

32=2402R32=\frac{240^2}{R}

R=240232R=\frac{240^2}{32}

R=1800ΩR=1800\Omega

Now we know that

R=ρlAR=\frac{\rho l}{A}

l=RAρl=\frac{RA}{\rho}


l=1800×3.14×(4.064×106)22.825×106=3.30×105ml=\frac{1800\times3.14\times(4.064\times10^{-6})^2}{2.825\times10^{-6}}=3.30\times10^{-5}m


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