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In a series LCR circuit, the inductance $L$ is $10\ mH$, capacitance $C$ is $1\ \mu F$ and resistance $R$ is $100\ \Omega$. The frequency at which resonance occurs is:
A
1.59 kHz
B
15.9 rad/s
C
15.9 kHz
D
1.59 rad/s
Explanation
At resonance $\omega=\frac{1}{\sqrt{LC}}=10^4\ rad/s$, so $f=1.59\ kHz$.
Detailed Solution
For resonance frequency: $\omega L=\frac{1}{\omega C}$
$\Rightarrow\omega=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{10\times10^{-3}\times1\times10^{-6}}}$
$=\frac{1}{\sqrt{10^{-8}}}=10^4\ rad/sec$
$f=\left(\frac{\omega}{2\pi}\right)=\frac{10^4}{2\pi}=1.59\ kHz$