Answer:
[tex]j_{B} = 917.454\,\frac{mA}{m^{2}}[/tex]
Explanation:
The current can be calculated by mutiplying the current density by cross section area. The new current density is obtained by the following relation and considering that same current flows through the new wire:
[tex]j_{A}\cdot A_{A} = j_{B}\cdot A_{B}[/tex]
[tex]j_{B} = j_{A}\cdot \frac{A_{A}}{A_{B}}[/tex]
[tex]j_{B} = j_{A} \cdot \left(\frac{D_{A}}{D_{B}} \right)^{2}[/tex]
[tex]j_{B} = \left(0.33\,\frac{mA}{m^{2}} \right)\cdot \left(\frac{2.9\,mm}{0.055\,mm} \right)^{2}[/tex]
[tex]j_{B} = 917.454\,\frac{mA}{m^{2}}[/tex]
The current density in the lightbulb's filament is [tex]917.454\frac{mA}{m^2}[/tex]
The current should be determined by multiplying the current density by cross section area. The new current density should be measured by the following relation and considering that the same current flows via the new wire.
So,
[tex]j_A.A_A=jB.A_B\\\\jB= jA.\frac{A_A}{A_B}\\\\ = 0.33 \times (\frac{2.99}{0.0550})^2\\\\= 917.454\frac{mA}{m^2}[/tex]
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