Problem — Natural frequency of an LC circuit

Problem

An ideal $LC$ circuit has $L=10\ \text{mH}$ and $C=1\ \mu\text{F}$. Calculate the natural frequency $f_0=\dfrac{1}{2\pi\sqrt{LC}}$.

Solution

Product $LC$: $LC=(10\cdot 10^{-3})(1\cdot 10^{-6})=10^{-8}\ \text{s}^2\ \Rightarrow\ \sqrt{LC}=10^{-4}\ \text{s}$

Natural frequency: $f_0=\frac{1}{2\pi\sqrt{LC}}=\frac{1}{2\pi\cdot 10^{-4}}=\frac{1}{6{,}28\cdot 10^{-4}}\approx 1{,}6\cdot 10^{3}\ \text{Hz}$ $\ev{f_0\approx 1{,}6\cdot 10^{3}\ \text{Hz}}$

Links

Topics: Electromagnetic induction Concepts: LC and RLC oscillations · Resonance