Is this a complete Tesla coil simulation?

No. Real coils are strongly nonlinear: spark gaps quench and re‑ignite, top‑load capacitance and streamers change the effective **C₂**, and losses are more complex. This model is a **linear** coupled RLC teaching tool that captures the **resonant transformer** idea.

Why can V_C₂ exceed the drive amplitude V₀?

With light damping on the secondary and coupling near resonance, energy stored in the **L₂C₂** tank can accumulate across many cycles—similar to any driven resonator—even though the instantaneous input is modest. The ratio is not limited to an ideal transformer turns ratio because the dynamics are resonant, not purely sinusoidal steady state at a single frequency with infinite Q.

How does this relate to the Mutual Inductance page?

The mutual‑inductance page uses **RL** loops without capacitors. Adding **C₁** and **C₂** introduces **second‑order** dynamics and resonant peaks; the coupled equations generalize naturally from that starting point.

What do R₁ and R₂ represent?

They bundle winding resistance, radiation, and other losses into simple Ohmic terms so the model stays low‑dimensional. Raising **R₂** lowers the secondary Q and suppresses excessive ringing.

Resonant Transformer (Tesla-style)

A Tesla coil or resonant transformer is often explained as two magnetically coupled resonant circuits: a primary L₁C₁ tank driven by an RF source, and a high‑Q secondary L₂C₂ that can develop very large voltages when the drive frequency is close to its natural resonance. This page solves the linear coupled RLC differential equations with mutual inductance M = k√(L₁L₂): in charge–current form, L₁q₁″ + Mq₂″ + R₁q₁′ + q₁/C₁ = V(t) and Mq₁″ + L₂q₂″ + R₂q₂′ + q₂/C₂ = 0 for a grounded secondary reference with no independent source. The drive V(t) = V₀ sin(ωt) is applied on the primary loop. Students can read the small‑signal resonant frequencies f₀₁ = 1/(2π√(L₁C₁)) and f₀₂ = 1/(2π√(L₂C₂)), tune ω, adjust k, and watch how V_C₂ = q₂/C₂ grows when the system is brought near secondary resonance and coupling transfers energy efficiently. Important limitations: there is no spark gap, no streamer/corona physics, no distributed capacitance or arc loading—only a textbook coupled‑tank model. Decorative “sparks” on the canvas are a qualitative visual tied to |V_C₂|, not a breakdown calculation.

Who it's for: Advanced high-school and undergraduate electromagnetics students comparing ideal transformers, mutual inductance, and resonant energy transfer.

Key terms

Mutual inductance
Coupled oscillators
Resonance
Quality factor
Tesla coil (schematic)
Primary and secondary tanks
Coupling coefficient
Capacitor voltage

Live graphs

How it works

Loosely coupled resonant circuits transfer energy at the drive frequency; when f_drive is near the secondary ω₀, capacitor voltage on the high‑Q side can grow large — the idea behind a resonant transformer / Tesla coil schematic.

Key equations

ω₀ = 1/√(LC), M = k√(L₁L₂)

L₁q₁″ + Mq₂″ + R₁q₁′ + q₁/C₁ = V(t), Mq₁″ + L₂q₂″ + R₂q₂′ + q₂/C₂ = 0

Frequently asked questions

Is this a complete Tesla coil simulation?: No. Real coils are strongly nonlinear: spark gaps quench and re‑ignite, top‑load capacitance and streamers change the effective C₂, and losses are more complex. This model is a linear coupled RLC teaching tool that captures the resonant transformer idea.
Why can V_C₂ exceed the drive amplitude V₀?: With light damping on the secondary and coupling near resonance, energy stored in the L₂C₂ tank can accumulate across many cycles—similar to any driven resonator—even though the instantaneous input is modest. The ratio is not limited to an ideal transformer turns ratio because the dynamics are resonant, not purely sinusoidal steady state at a single frequency with infinite Q.
How does this relate to the Mutual Inductance page?: The mutual‑inductance page uses RL loops without capacitors. Adding C₁ and C₂ introduces second‑order dynamics and resonant peaks; the coupled equations generalize naturally from that starting point.
What do R₁ and R₂ represent?: They bundle winding resistance, radiation, and other losses into simple Ohmic terms so the model stays low‑dimensional. Raising R₂ lowers the secondary Q and suppresses excessive ringing.

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Frequently asked questions

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