Answer :
Answer :
The time is 0.46 sec.
Explanation:
Given that,
Diameter = 0.30 mm
Voltage = 1.5 V
Length = 5.5 cm
Resistivity of gold [tex]\rho= 2.44\times10^{-8}\ \Omega m[/tex]
We know that,
The resistance is
[tex]R=\dfrac{\rho L}{A}[/tex]...(I)
The current is
[tex]I=\dfrac{V}{R}[/tex]...(II)
Put the value of R
[tex]I=\dfrac{V}{\dfrac{\rho L}{A}}[/tex]
[tex]I=\dfrac{VA}{\rho L}[/tex]
We need to calculate the drift velocity
Using formula of drift velocity
[tex]v_{d}=\dfrac{I}{neA}[/tex]
[tex]v_{d}=\dfrac{\dfrac{VA}{\rho L}}{neA}[/tex]
[tex]v_{d}=\dfrac{V}{ne\rho L}[/tex]
Put the value into the formula
[tex]v_{d}=\dfrac{1.5}{5.90\times10^{28}\times1.6\times10^{-19}\times5.5\times10^{-2}\times2.44\times10^{-8}}[/tex]
[tex]v_{d}=11.8\times10^{-2}\ cm/s[/tex]
We need to calculate the time
Using formula of time
[tex]t=\dfrac{L}{v_{d}}[/tex]
Put the value into the formula
[tex]t=\dfrac{5.5}{11.8\times10^{-2}}[/tex]
[tex]t=0.46\ sec[/tex]
Hence, The time is 0.46 sec.