Answer to Question #314635 in Electric Circuits for John

Question

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

Answer 1

Power

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

$P=\frac{8}{0.25}=32W$

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

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

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

$R=1800\Omega$

Now we know that

$R=\frac{\rho l}{A}$

$l=\frac{RA}{\rho}$

$$l=\frac{1800\times3.14\times(4.064\times10^{-6})^2}{2.825\times10^{-6}}=3.30\times10^{-5}m$$