he current in a 100 watt lightbulb is 0.840 A. The filament inside the bulb is 0.140 mm in diameter.
a) What is the current density in the filament?
b) What is the electron current in the filament?
To answer these questions, we need to use two formulas: Ohm's Law and the formula for current density.
a) To find the current density in the filament, we can use the formula for current density:
Current Density (J) = Current (I) / Cross-sectional Area (A)
We are given the current in the bulb, which is 0.840 A.
To find the cross-sectional area of the filament, we need to use the formula for the area of a circle:
Area (A) = π * (radius)^2
We are given the diameter of the filament, which is 0.140 mm. To find the radius, we divide the diameter by 2:
Radius = 0.140 mm / 2 = 0.070 mm
Now, we convert the radius to meters by dividing by 1000 since 1 mm = 0.001 m:
Radius = 0.070 mm / 1000 = 0.000070 m
Substituting the values into the formula, we get:
Area (A) = π * (0.000070)^2
Now, we can calculate the current density:
Current Density (J) = 0.840 A / [π * (0.000070)^2]
b) To find the electron current in the filament, we can use the formula for current (I) in terms of electron charge (e) and time (t):
Current (I) = Charge (Q) / Time (t)
We are given the power of the bulb, which is 100 watts. We can use the formula for power in terms of current (I) and voltage (V):
Power (P) = Current (I) * Voltage (V)
Given that the power is 100 watts and the current is 0.840 A, we can rearrange the formula to find the voltage:
Voltage (V) = Power (P) / Current (I)
Now, we can calculate the voltage by substituting the values:
Voltage (V) = 100 / 0.840
Once we have the voltage, we can calculate the electron current by using the formula:
Current (I) = Charge (Q) / Time (t)
We know the charge of an electron is 1.6 x 10^-19 coulombs, and we can rearrange the formula to solve for charge:
Charge (Q) = Current (I) * Time (t)
Since the question does not provide a specific time duration, we cannot calculate the electron current without knowing the time.