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title: "An ideal LC circuit consists of a capacitor of capacitance \\(C\\) connected to an air-core inductor of self-inductance \\(L\\). The capacitor is initially charged, and an oscilloscope connected across the capacitor displays a sinusoidal voltage waveform of period \\(T\\). A ferromagnetic iron core of relative permeability \\(\\mu_r > 1\\) is then fully inserted into the interior of the inductor coil. Which of the following correctly describes how the observed period of oscillation of the capacitor voltage changes, and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/121305/"
date_modified: "2026-08-23T04:59:39+00:00"
---

# An ideal LC circuit consists of a capacitor of capacitance \(C\) connected to an air-core inductor of self-inductance \(L\). The capacitor is initially charged, and an oscilloscope connected across the capacitor displays a sinusoidal voltage waveform of period \(T\). A ferromagnetic iron core of relative permeability \(\mu_r > 1\) is then fully inserted into the interior of the inductor coil. Which of the following correctly describes how the observed period of oscillation of the capacitor voltage changes, and provides the correct justification?

An ideal LC circuit consists of a capacitor of capacitance \(C\) connected to an air-core inductor of self-inductance \(L\). The capacitor is initially charged, and an oscilloscope connected across the capacitor displays a sinusoidal voltage waveform of period \(T\). A ferromagnetic iron core of relative permeability \(\mu_r > 1\) is then fully inserted into the interior of the inductor coil. Which of the following correctly describes how the observed period of oscillation of the capacitor voltage changes, and provides the correct justification?

![A schematic diagram showing a closed single-loop circuit. On the left vertical branch is a parallel-plate capacitor labeled \(C\). On the right vertical branch is a helical inductor labeled \(L\). Directly above the inductor is a solid shaded rectangular bar labeled iron core, with a straight downward arrow indicating insertion into the center of the inductor. Two probe leads extend from across the capacitor terminals to an oscilloscope screen displaying a single continuous sinusoidal voltage waveform.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461179-fSyvtD.jpg)

- **A.** The period of oscillation decreases because the iron core increases the magnetic flux density, causing energy to transfer between the electric and magnetic fields at a higher rate.
- **B.** The period of oscillation decreases because the alignment of magnetic domains inside the iron core opposes the induced EMF, thereby lowering the effective self-inductance of the inductor.
- **C.** The period of oscillation increases because the iron core introduces eddy-current damping that broadens the voltage resonance curve and increases the time between successive zero-crossings.
- **D.** The period of oscillation increases because the iron core increases the self-inductance \(L\), which reduces the rate of current change \(\left|\dfrac{dI}{dt}\right| = \dfrac{V_L}{L}\) for a given voltage and lengthens the time required to cycle charge between the capacitor plates.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121305/*