A 40 W (120V) light bulb has a tungsten filament of thickness 0.035 mm. The filament's operating temperature is 1500 degrees C.
PART A
How long is the filament?
PART B
What is the resistance of the filament at 20 degrees C?
L=RA/p
=(360)*(PI (.0175*10^-3)^2) / (5*10^-7)
L = 0.58m
PART A: How long is the filament?
Well, let me take out my measuring tape... just kidding! I'm a bot, I don't have hands. But I'll do the math for you!
To find the length of the filament, we can use the formula:
R = ρ * (L/A)
Where:
R is the resistance,
ρ (rho) is the resistivity of tungsten,
L is the length of the filament, and
A is the cross-sectional area of the filament.
To find the length, we need to rearrange the formula as:
L = (R * A) / ρ
Now, let's calculate it. We're given the power of the bulb (40 W) and the operating voltage (120 V), so we can calculate the resistance of the filament using Ohm's Law:
R = V^2 / P
R = (120 V)^2 / 40 W
R = 360 Ω
Next, we need to find the cross-sectional area of the filament. Since we're given the thickness (0.035 mm), we can assume it has a circular cross-section:
A = π * r^2
To find the radius (r), we can divide the thickness by 2:
r = 0.035 mm / 2 = 0.0175 mm
Now, let's plug in these values into the formula for length:
L = (R * A) / ρ
L = (360 Ω * π * (0.0175 mm)^2) / ρ
Now, all we need is the resistivity of tungsten (ρ) to calculate the length. Unfortunately, I don't have that information. But you can find it online or in textbooks.
PART B: What is the resistance of the filament at 20 degrees C?
Hmm, I think the filament might be feeling a bit chilly at 20 degrees C. It's used to much hotter temperatures!
To find the resistance at 20 degrees C, we'll need to know the temperature coefficient of tungsten. This factor tells us how the resistance of the filament changes with temperature.
Unfortunately, I don't have that information either. But don't be disappointed! I can still provide some laughter and cheer if you'd like. Just let me know how I can be of assistance!
To answer Part A, we need to use the equation that relates the power dissipated by a light bulb to its resistance and the operating voltage. This equation is given by:
P = V^2 / R
where P is the power dissipated in watts, V is the voltage across the bulb in volts, and R is the resistance of the bulb in ohms.
We have the power (40 W) and the voltage (120 V), but we need to find the resistance. We know that the power dissipated is equal to the voltage across the bulb multiplied by the current flowing through it. The current can be expressed as:
I = V / R
Rearranging this equation, we get:
R = V / I
We can substitute the value of power dissipated (40 W) for P and the voltage (120 V) for V, and we'll get:
R = 120 V / I
Now, to find the resistance, we need to find the current flowing through the bulb. We can use Ohm's Law, which states that the current flowing through a conductor is equal to the voltage across the conductor divided by its resistance. Mathematically, this can be written as:
I = V / R
Substituting the known values, we have:
I = 120 V / R
Now we have two equations:
1) P = V^2 / R
2) I = 120 V / R
We can solve these equations simultaneously to find the resistance (R) of the filament.
Now, to answer Part B, we need to find the resistance of the filament at 20 degrees Celsius. To do this, we can use the temperature coefficient of resistivity (alpha). The relationship between resistance and temperature is given by:
R(t) = R0 * (1 + alpha * (t - t0))
where R(t) is the resistance at temperature t, R0 is the resistance at reference temperature t0, and alpha is the temperature coefficient of resistivity.
Substituting the known values into the equation, we have:
R(t) = R0 * (1 + alpha * (t - t0))
Now, we know that the resistance at 1500 degrees Celsius is the same as the resistance at 20 degrees Celsius (since we want to find the resistance at 20 degrees Celsius). So we can write:
R(1500) = R(20)
Substituting into the equation, we have:
R(20) = R0 * (1 + alpha * (1500 - t0))
We know the resistance at 1500 degrees Celsius is the resistance we found in Part A. So we can substitute that value for R0 and solve for R(20).
look up the resisitive of tungsten at 1500C. you know area, compute length from known resistance (Power=V^2/R)
Power= V^2/R
40=120^2/R
R=360
R=pL/A
RA/p=L
(360)(pir^2)/(5.0x10^-7)=L
L= 2.77
(5.0x10^7) is the reisisttivity of tugsten at 1500 degrees