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Electric Current in Conductors — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsElectric Current in Conductors5 Marks
Question
A copper wire of radius 0.1mm and resistance $1\text{k}\Omega$ is connected across a power supply of 20V.
(a) How many electrons are transferred per second between the supply and the wire at one end? (b) Write down the current density in the wire.
✓

Answer

$\text{r}=0.1\text{mm}=10^{-4}\text{m}$$\text{R}=1\text{K}\Omega=10^3\Omega,\text{V}=20\text{V}$
  1. No.of electrons transferred
$\text{i}=\frac{\text{V}}{\text{R}}=\frac{20}{10^3}=20\times10^{-3}=2\times10^{-2}\text{A}$
$\text{q}=\text{it}=2\times10^{-2}\times1=2\times10^{-2}\text{C}$
No. of electrons transferred $=\frac{2\times10^{-2}}{1.6\times10^{-19}}=\frac{2\times10^{-17}}{1.6}=1.25\times10^{17}.$
  1. Current density of wire
​​​​​​​​​​​​​​​​​​​​​$=\frac{\text{i}}{\text{A}}=\frac{2\times10^{-2}}{\pi\times10^{-8}}=\frac{2}{3.14}\times10^6$
$=0.6369\times10^6=6.37\times10^5\text{A}/\text{m}^2.$

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