Physics - EMI/AC Question with Solution | TestHub

as given $Z=\sqrt{{\left(X_L-X_C\right)}^2+R^2}$

$X_L={\omega }_L=100\times 100\times 10^{-3}=10\Omega$

$X_C=\frac{1}{{\omega }_C}=\frac{1}{100\times 100\times 10^{-6}}=100\Omega$

$Z=\sqrt{{\left(10-100\right)}^2+R^2}=\sqrt{90^2+120^2}$ $=30\times 5=150\Omega$

$i_{peak}=\frac{Vpeak}{z}=\frac{30}{150}=\frac{1}{5}amp=0.2amp$

$\&$ For resonant frequency

$\Rightarrow \omega L=\frac{1}{\omega \mathrm{C}}\Rightarrow {\omega }^2=\frac{1}{L\mathrm{C}}\Rightarrow \omega =\frac{1}{\sqrt{L\mathrm{C}}}$

$\&f=\frac{1}{2\pi \sqrt{L\mathrm{C}}}\Rightarrow \frac{1}{2\pi \sqrt{100\times 10^{-3}\times 100\times 10^{-6}}}$

$=\frac{100\sqrt{10}}{2\pi }=\frac{100\pi }{2\pi }=50\text{Hz}$

as $\sqrt{10}\approx \pi$