In (R-C) circuit (\omega=100, rad ,s ^{-1},, R =100, \Omega,... | Physics | SolveeIt

Question

In $R-C$ circuit $\omega=100\, rad \,s ^{-1},\, R =100\, \Omega,\, C =20\, \mu\, F$ . What is impedance?

$510\,\Omega$

$200\, \Omega$

$250\, \Omega$

$300\, \Omega$

Answer

$510\,\Omega$

Explanation

Solution

Impedance for an R-C circuit is given by
$Z =\sqrt{R^{2}+X_{C}^{2}}=\sqrt{R^{2}+\left(\frac{1}{\omega C}\right)^{2}}$
$=\sqrt{(100)^{2}+\left(\frac{1}{100 \times 20 \times 10^{-6}}\right)^{2}}$
$=\sqrt{10^{4}+25 \times 10^{4}}$
$=100 \sqrt{26}$
$=510\, \Omega$

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