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
R=120/2.36
= 50.84745766
so the length of wire is
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
=
To find the length of the wire, let's follow these steps:
Step 1: Calculate the cross-sectional area of the wire.
The formula for the cross-sectional area of a circle is A = πr^2. Given that the radius (r) of the wire is 0.00464 mm, we need to convert it to meters by dividing by 1000:
r = 0.00464 mm = 0.00464/1000 m = 0.00000464 m
Now we can calculate the area:
A = π(0.00000464)^2 = 0.0000000215296 m^2
Step 2: Calculate the resistance per meter.
The resistivity (ρ) of the wire is given as 5.6 x 10^-8 Ω·m. The resistance per meter (P) can be calculated using the formula:
P = ρ/A = 5.6 x 10^-8 Ω·m / 0.0000000215296 m^2 = 2.59610215 Ω/m
Step 3: Calculate the length of the wire.
We know that the resistance (R) is equal to the voltage (V) divided by the current (I). In this case, the voltage is 120 V and the current is 2.36 A:
R = V/I = 120 V / 2.36 A = 50.84745766 Ω
Now we can rearrange the formula to solve for the length (L):
L = R/P = 50.84745766 Ω / 2.59610215 Ω/m = 19.5979 meters
So, the length of the wire must be approximately 19.5979 meters.
To find the length of the wire, we can use Ohm's law which states that the resistance (R) is equal to the resistivity (ρ) times the length of the wire (L) divided by the cross-sectional area (A).
Given:
Resistivity, ρ = 5.6 x 10^-8 Ω·m
Radius of the wire, r = 0.00464 mm = 0.00464 x 10^-3 m
Voltage, V = 120 V
Current, I = 2.36 A
To find the cross-sectional area (A):
A = πr^2
A = π(0.00464 x 10^-3)^2
A ≈ 6.751 x 10^-11 m^2
To find the resistance (R):
R = ρ(L/A)
We can rearrange the formula to solve for L:
L = (RA)/ρ
Substituting the given values:
L = ((6.751 x 10^-11) x (120/2.36))/(5.6 x 10^-8)
Calculating L:
L ≈ 0.000135 m
So, the length of the wire must be approximately 0.000135 meters.