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title: "Circuit 1 consists of an ideal capacitor of capacitance \\(C\\) connected in series with two ideal inductors of inductance \\(L\\) and \\(3L\\), with no mutual inductance between them. Circuit 2 consists of an identical capacitor of capacitance \\(C\\) connected in parallel with two ideal inductors of inductance \\(L\\) and \\(3L\\), also with no mutual inductance. Both circuits undergo simple harmonic electromagnetic oscillations. What is the ratio \\(T_1 / T_2\\) of the period of oscillation of Circuit 1 to the period of oscillation of Circuit 2?"
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url: "https://nerd-notes.com/ubq/118691/"
date_modified: "2026-08-04T08:13:47+00:00"
---

# Circuit 1 consists of an ideal capacitor of capacitance \(C\) connected in series with two ideal inductors of inductance \(L\) and \(3L\), with no mutual inductance between them. Circuit 2 consists of an identical capacitor of capacitance \(C\) connected in parallel with two ideal inductors of inductance \(L\) and \(3L\), also with no mutual inductance. Both circuits undergo simple harmonic electromagnetic oscillations. What is the ratio \(T_1 / T_2\) of the period of oscillation of Circuit 1 to the period of oscillation of Circuit 2?

Circuit 1 consists of an ideal capacitor of capacitance \(C\) connected in series with two ideal inductors of inductance \(L\) and \(3L\), with no mutual inductance between them. Circuit 2 consists of an identical capacitor of capacitance \(C\) connected in parallel with two ideal inductors of inductance \(L\) and \(3L\), also with no mutual inductance. Both circuits undergo simple harmonic electromagnetic oscillations. What is the ratio \(T_1 / T_2\) of the period of oscillation of Circuit 1 to the period of oscillation of Circuit 2?

![Two separate circuit schematics placed side-by-side. On the left, Circuit 1 is a single rectangular loop containing a capacitor labeled C, an inductor labeled L, and a second inductor labeled 3L, all connected in series by wire lines. On the right, Circuit 2 shows a capacitor labeled C connected in series with a parallel combination consisting of two parallel wire branches, one branch containing an inductor labeled L and the other branch containing an inductor labeled 3L. No other components, text, or arrows appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831226-8QLpC8.jpg)

- **A.** \(\dfrac{\sqrt{3}}{4}\)
- **B.** \(\dfrac{2\sqrt{3}}{3}\)
- **C.** \(\dfrac{4}{3}\)
- **D.** \(\dfrac{4\sqrt{3}}{3}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118691/*