Question 41 of 190

Find the peak current and resonant frequency of the following circuit (as shown in figure).

A$2A$ and $50Hz$B$0.2A$ and $100Hz$C$2A$ and $100Hz$D$0.2A$ and $50Hz$

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Answer: (D) $0.2A$ and $50Hz$

as given $Z=\sqrt{{\left({X}_{L}-{X}_{C}\right)}^{2}+{R}^{2}}$
${X}_{L}={\omega }_{L}=100\times 100\times {10}^{-3}=10\Omega$
${X}_{C}=\dfrac{1}{{\omega }_{C}}=\dfrac{1}{100\times 100\times {10}^{-6}}=100\Omega$
$Z=\sqrt{{\left(10-100\right)}^{2}+{R}^{2}}=\sqrt{{90}^{2}+{120}^{2}}$$=30\times 5=150\Omega$
${i}_{peak}=\dfrac{Vpeak}{z}=\dfrac{30}{150}=\dfrac{1}{5}amp=0.2amp$
& For resonant frequency
$\Rightarrow \omega L=\dfrac{1}{\omega C}\Rightarrow {\omega }^{2}=\dfrac{1}{LC}\Rightarrow \omega =\dfrac{1}{\sqrt{LC}}$
&f=\dfrac{1}{2\pi \sqrt{LC}}\Rightarrow \dfrac{1}{2\pi \sqrt{100\times {10}^{-3}\times 100\times {10}^{-6}}}
$=\dfrac{100\sqrt{10}}{2\pi }=\dfrac{100\pi }{2\pi }=50Hz$
as $\sqrt{10}\approx \pi$

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