The filament in an incandescent light bulb is made from tungsten (resistivity 5.6 x 10-8 Ù·m). The light bulb is plugged into a 120-V outlet and draws a current of 2.36 A. If the radius of the tungsten wire is 0.00464 mm, how long must the wire be?
restivity of the wire = 5.6 x 10-8 Ù·m
the cross sectional area (in m^2) of the wire is
A=pi x (5.6 x 10-8)^2 =2304
so the resistamce per metre is
P/A (units ohm/m)
if the bulb draws 2.36A from 120 V then the resistance, R, is
R=120/2.36
= 50.84745766
so the length of wire is
R/(P/A)=RA/P
am I on the right path, sorry 5 hrs of this is getting to me lol
restivity of the wire = 5.6 x 10-8 Ù·m
the cross sectional area (in m^2) of the wire is
A=pi x (0.00464)^2 = 0.0000215296
so the resistamce per metre is
P/A (units ohm/m)
if the bulb draws 2.36A from 120 V then the resistance, R, is
R=120/2.36
= 50.84745766
so the length of wire is
50.84745766/(0.000000056)=50.84745766*0.0000215296/P
907990315.357=0.00109472542/P
=
R=pL/A
R is resistance
P is resistivity
L is length
A is area
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The length of the wire is given by:
Length = Resistance x Area / Resistivity
Substituting the values:
Length = (50.84745766 ohm) x (2304 m^2) / (5.6 x 10^-8 ohm·m)
Calculating:
Length = 2064384.169 m / (5.6 x 10^-8 ohm·m)
Length = 36897804643.75 m
Therefore, the length of the tungsten wire must be approximately 36,897,804,643.75 meters.
To find the length of the wire, we can use Ohm's Law which states that the resistance (R) is equal to the voltage (V) divided by the current (I). In this case, the resistance is already calculated as 50.84745766 ohms.
Now let's substitute the values into the formula:
Length of wire (L) = Resistance (R) / Resistivity (P/A)
L = 50.84745766 / (5.6 x 10^(-8))
L = 9.0801 x 10^8 meters
Therefore, the length of the tungsten wire must be approximately 9.0801 x 10^8 meters.