Question

The current in a 100 watt lightbulb is 0.900 A . The filament inside the bulb is 0.280 mm in diameter. 1-What is the current density in the filament? (with units) 2-What is the electron current in the filament? (with units)

Answer 1

Concepts and reason

The concepts used to solve this problem are current density and electric current.

Initially use the current density acts on the filament inside the bulb, by using current passing through the bulb and area of cross section of the bulb, then calculate the electron current in the filament by using current in the light bulb and charge of the electron.

Fundamentals

The expression for the current density in the filament acts inside the bulb is,

Here, J is the current density, I is the current flows in the filament, and A is the area of the filament inside the bulb.

The area of the bulb is,

Here, d is the diameter of the filament inside the bulb.

The expression for the electron current passing through the filament is,

Here, is the electron current and e is the charge of an electron.

(1)

The area of the bulb is,

Substitute for d to find A.

The current density in the filament acts inside the bulb is,

Substitute for I and for A to find J.

(2)

The electron current passing through the filament is,

Substitute for I and for e to find .

Ans: Part 1

The current density in the filament is.

Part 2

The electron current flow in the filament is.