Question

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

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

Answer 1

Answer: (A)

as given $z=\sqrt{{\left(x_L-x_C\right)}^2+R^2}$
$x_L={\omega }_L=100\times 100\times 10^{-3}=10\Omega$
$x_C=\frac{1}{{\omega }_C}=\frac{1}{100\times 100\times 10^{-6}}=10\Omega$
$z=\sqrt{(10-100{)}^2+R^2}=\sqrt{90^2+120^2}$
$=30\times 5=150\Omega$
$i_{peak}=\frac{\Delta v}{z}=\frac{30}{150}=\frac{1}{5}amp=0.2amp$
& For resonant frequency
$\Rightarrow \omega L=\frac{1}{\omega C}\Rightarrow {\omega }^2=\frac{1}{LC}\Rightarrow \omega =\frac{1}{\sqrt{LC}}$
$\&f=\frac{1}{2\pi \sqrt{LC}}\Rightarrow \frac{1}{2\pi \sqrt{100\times 10^{-3}\times 100\times 10^{-6}}}$
$=\frac{100\sqrt{10}}{2\pi }=\frac{100\pi }{2\pi }=50Hz$
as $\sqrt{10}\approx \pi$