Answer to Question #308658 in Physics for chan

Question #308658

If the 0.100-mm-diameter tungsten filament in a light bulb is to have a resistance of 0.300 \OmegaΩ at 20.0 ^o


o


C , how long should it be?

1
Expert's answer
2022-03-13T18:50:00-0400

The length is given as follows:


l=ARρl = \dfrac{AR}{\rho}

where A=πd2/4A = \pi d^2/4 is the area of the filament cross-section, d=0.1mm=0.1×103md = 0.1mm = 0.1\times 10^{-3}m is the diameter, R=0.3ΩR = 0.3\Omega is the resistance, and ρ=5.6×108Ωm\rho = 5.6\times 10^{-8}\Omega \cdot m is electrical resistivity of tungsten. Thus, obtain:


l=πd2R4ρl=π(0.1×103)20.345.6×1080.0421m=4.21cml = \dfrac{\pi d^2R}{4\rho}\\ l = \dfrac{\pi \cdot (0.1\times 10^{-3})^2\cdot 0.3}{4\cdot 5.6\times 10^{-8}} \approx 0.0421m = 4.21cm

Answer. 4.21 cm.


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