Physics

Resonant frequency in an RLC circuit depends on the relationship between inductance and capacitance through $f_0 = \frac{1}{2\pi\sqrt{LC}}$. The key insight is recognizing how frequency scales when you change capacitance: since $f$ is inversely proportional to $\sqrt{C}$, increasing capacitance by a factor of 5 means the frequency decreases by a factor of $\sqrt{5}$. You don't need to know $L$ or the actual resistance—just use the ratio of the two frequencies.

Resonant frequency in an RLC circuit depends on the relationship between inductance and capacitance through $f_0 = \frac{1}{2\pi\sqrt{LC}}$. The key insight is recognizing how frequency scales when you change capacitance: since $f$ is inversely proportional to $\sqrt{C}$, increasing capacitance by a factor of 5 means the frequency decreases by a factor of $\sqrt{5}$. You don't need to know $L$ or the actual resistance—just use the ratio of the two frequencies.