A parallel$-$plate capacitor with plate area $20\ cm^2$ and plate separation $1.0\ mm$ is connected to a battery. The resistance of the circuit is $10\text{k}\Omega.$ Find the time constant of the circuit.
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$\text{A}=20\text{cm}^2=20\times10^{-4}\text{m}^2$
$\text{d}=1\text{mm}=1\times10^{-3}\text{m};\text{R}=10\text{K}\Omega$
$\text{C}=\frac{\text{E}_0\text{A}}{\text{d}}=\frac{8.85\times10^{-12}\times20\times10^{-4}}{1\times10^{-3}}$
$=\frac{8.85\times10^{-12}\times2\times10^{-3}}{10^{-3}}=17.7\times10^{-2}$ Farad.
Time constant $=\text{CR}=17.7\times10^{-2}\times10\times10^3$
$=17.7\times10^{-8}=0.177\times10^{-6}\text{s}=0.18\mu\text{s}.$
$\text{d}=1\text{mm}=1\times10^{-3}\text{m};\text{R}=10\text{K}\Omega$
$\text{C}=\frac{\text{E}_0\text{A}}{\text{d}}=\frac{8.85\times10^{-12}\times20\times10^{-4}}{1\times10^{-3}}$
$=\frac{8.85\times10^{-12}\times2\times10^{-3}}{10^{-3}}=17.7\times10^{-2}$ Farad.
Time constant $=\text{CR}=17.7\times10^{-2}\times10\times10^3$
$=17.7\times10^{-8}=0.177\times10^{-6}\text{s}=0.18\mu\text{s}.$
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