Current and Ohm's Law-filament diameter

In summary, Ohm's Law and the current in a standard 100 W (120 V) lightbulb with a 8.50 cm-long tungsten filament can be calculated using the equations Power = I * DeltaV = Delta^2/R and J = I/A, where J represents the current density and A is the area. To solve for the diameter of the filament, the high-temperature resistivity of tungsten (rho) and the specific resistivity (sigma) can be used.
  • #1
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current and Ohm's Law--filament diameter

Homework Statement



A standard 100 W (120 V ) lightbulb contains a 8.50 cm -long tungsten filament. The high-temperature resistivity of tungsten is 9.0*10^-7.

Homework Equations


Power=I[tex]\Delta[/tex]V=[tex]\Delta[/tex]^2/R
J=I/A

The Attempt at a Solution



I know power, [tex]\Delta[/tex]V, and R and am solving for either r or d.
I can use the first equation to solve for I. And then I want to use the second equation because it is the only equation that I've found that uses area (and thus r and d), but I don't know J. Any suggestions? Thanks!
 
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  • #2


(solving for diameter of filament, in micrometers)
 
  • #3


Maybe I use sigma and rho?
 

Related to Current and Ohm's Law-filament diameter

1. What is the relationship between current and filament diameter?

The relationship between current and filament diameter is described by Ohm's Law. According to Ohm's Law, the current through a conductor is directly proportional to the voltage and inversely proportional to the resistance. Therefore, as the filament diameter increases, the resistance of the filament decreases, leading to an increase in current.

2. How does the filament diameter affect the resistance of a wire?

The filament diameter has a direct impact on the resistance of a wire. As the diameter of the filament increases, the resistance of the wire decreases. This is due to the fact that a larger diameter means more space for electrons to flow through, resulting in less resistance to the current.

3. What is the significance of current and Ohm's Law in relation to filament diameter?

Current and Ohm's Law are essential concepts in understanding the relationship between filament diameter and resistance in a wire. They help us understand how changing the filament diameter can impact the flow of current and the resistance of the wire. This knowledge is crucial in various applications, such as designing electrical circuits and determining appropriate wire sizes for different purposes.

4. How do you calculate the current and resistance of a wire with a given filament diameter?

To calculate the current and resistance of a wire with a given filament diameter, you can use Ohm's Law. The formula for Ohm's Law is I = V/R, where I is the current in amperes, V is the voltage in volts, and R is the resistance in ohms. By rearranging the formula, you can calculate the resistance as R = V/I. Therefore, to find the current, you would divide the voltage by the resistance, and to find the resistance, you would divide the voltage by the current.

5. How does temperature affect the relationship between current and filament diameter?

Temperature can impact the relationship between current and filament diameter. As the temperature of a wire increases, the resistance also increases. This means that as the temperature rises, the current decreases for a given filament diameter. This is because as the temperature increases, the atoms in the wire vibrate more, causing more resistance to the flow of electrons. Therefore, the relationship between current and filament diameter is affected by the temperature of the wire.

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