An LC series circuit with an inductance L and a capacitance C has an oscillation frequency f.If we now take two of those inductors, each with inductance L, and two of the capacitors, each with capacitance C, and wire them all in series to make a new circuit, its oscillation frequency will be:
A)f/4
B)f/2
C)f
D)2f
E)4f

Question

Quizplus · Accepted Answer

The oscillation frequency of an LC circuit is given by $f = \frac{1}{2\pi\sqrt{LC}}$. When the inductors and capacitors are wired in series, the total inductance is $2L$ and the total capacitance is $2C$. Substituting these into the formula gives $f' = \frac{1}{2\pi\sqrt{2L \cdot 2C}} = \frac{1}{2\sqrt{2}\pi\sqrt{LC}}$, which simplifies back to the original frequency $f$. Therefore, the oscillation frequency remains unchanged.

An LC Series Circuit with an Inductance L and a Capacitance