--- title: "Oscillations in LC and RLC Circuits" description: "Charge sloshing between a capacitor and an inductor obeys the same equation as a mass on a spring, with resistance playing the part of damping. The electrical and mechanical problems share every solut" canonical: https://lightmysky.com/learn/science/oscillations-in-lc-and-rlc-circuits-mt_QJsqX7xzkZ source: https://lightmysky.com/learn/science/oscillations-in-lc-and-rlc-circuits-mt_QJsqX7xzkZ.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Oscillations in LC and RLC Circuits Charge sloshing between a capacitor and an inductor obeys the same equation as a mass on a spring, with resistance playing the part of damping. The electrical and mechanical problems share every solution. Subject: Science · Area: Electricity & Magnetism · Ages 20 to 21 Page: https://lightmysky.com/learn/science/oscillations-in-lc-and-rlc-circuits-mt_QJsqX7xzkZ ## Ready when they can - Derives the LC equation from the loop rule and identifies the resonant frequency - Matches charge, current, inductance and capacitance to displacement, velocity, mass and spring constant - Describes how resistance damps the oscillation and where the energy goes ## Lesson: Charge on a spring: LC ringing and RLC damping A capacitor wired to an inductor forms an LC circuit, a mass on a spring made of fields. Start with a charged capacitor: it discharges through the coil, current peaks as charge hits zero, then the coil keeps pushing charge onto the other plate. Energy sloshes between electric and magnetic storage at omega0 equals 1 over sqrt(LC). One loop-rule line gives d squared q/dt squared plus (1/LC) q equals 0, the same equation as a spring. **Example.** Map each electrical piece to its mechanical twin and every spring result ports over free. Charge plays position, current plays velocity, L plays mass, and 1 over C plays spring stiffness. Sinusoids, phase, and energy swapping all carry across unchanged. The total energy stays fixed at Qmax squared over 2C, trading between capacitor and inductor each quarter cycle. Add a resistor and the ringing dies: this is the series RLC circuit. Resistance siphons a little energy into heat each cycle, so the amplitude falls inside an exponential envelope while the oscillation continues near omega0. Light damping rings many cycles, critical damping settles fastest without overshoot, and heavy damping creeps back to rest. Tuning R against L and C picks the regime. **Tip.** Solve any LC or RLC question in this order. Write the loop equation and confirm it matches d squared q/dt squared plus (1/LC) q equals 0 for the ideal case. Read off omega0 equals 1 over sqrt(LC). Then weigh R against L and C to name the damping regime before touching any formula. **Recap.** An LC loop rings like a spring at 1 over sqrt(LC), charge maps to position and L to mass, and resistance drains the ringing as heat. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Self-Inductance and Energy Stored in a Magnetic Field](https://lightmysky.com/learn/science/self-inductance-and-energy-stored-in-a-magnetic-field-mt_BLyLSJT-Fr) - [Damped Oscillations and the Three Damping Regimes](https://lightmysky.com/learn/science/damped-oscillations-and-the-three-damping-regimes-mt_JCpYpFVn6s) - [Damped and Driven Oscillations](https://lightmysky.com/learn/mathematics/damped-and-driven-oscillations-mt_Y8K1njb1PH) ## Opens up - [Impedance and Phasors in AC Circuits](https://lightmysky.com/learn/science/impedance-and-phasors-in-ac-circuits-mt_vQVlVWv2ln)