The filament in an incandescent light bulb is made from tungsten. The light bulb is plugged into a 240 V outlet and draws a current of 1.16 A. If the radius of the tungsten wire is 0.0052 mm, how long must the wire be?
You need the restivity of the wire, lets say it is P ohm.m
the cross sectional area (in m^2) of the wire is
A=pi x (5.2x10^-6 m)^2
so the resistamce per metre is
P/A (units ohm/m)
if the bulb draws 1.16 A from 240 V then the resistance, R, is
R=240/1.16
so the length of wire is
R/(P/A)=RA/P
To calculate the length of the tungsten wire in the incandescent light bulb, we can use the formula for resistance:
Resistance (R) = Voltage (V) / Current (I)
Given that the voltage is 240 V and the current is 1.16 A, we can calculate the resistance of the tungsten wire:
R = 240 V / 1.16 A
Now we need to find the resistivity of tungsten. Resistivity is a material property that relates to how well a material resists the flow of electric current. The resistivity of tungsten is approximately 5.6 x 10^-8 Ω·m.
The resistance of a wire can be calculated using the formula:
R = (Resistivity * Length) / Cross-sectional area
We can rearrange this formula to solve for the length of the wire:
Length = (Resistance * Cross-sectional area) / Resistivity
The cross-sectional area of a wire can be calculated using the formula for the area of a circle:
Cross-sectional area = π * (radius^2)
Therefore, we can plug in the values and calculate the length of the tungsten wire:
Cross-sectional area = π * (0.0052 mm)^2
Convert the radius to meters: 0.0052 mm = 5.2 x 10^-6 m
Length = [(240 V / 1.16 A) * π * (5.2 x 10^-6 m)^2] / (5.6 x 10^-8 Ω·m)
Simplify the equation and calculate the length.