Corriente de desplazamiento

Compare wire and displacement currents while a capacitor charges or discharges.

About this tool

Explore a voltage step

Choose an example or set capacitance C, resistance R, initial capacitor voltage V₀ and source voltage V₁. At t = 0 the source changes to V₁ while the capacitor voltage remains V₀. Render prepares the interval 0…6τ. The time field and slider move the probe; playback advances by one time constant per real second. Reset time returns to t = 0 with the same curves. Changing a parameter requires a new render.

Ideal RC model

With τ = RC and u = t/τ, V_C = V₁ + (V₀ − V₁)e^−u, Q = CV_C, I_cond = (V₁ − V₀)e^−u/R, dV_C/dt = (V₁ − V₀)e^−u/τ, I_d = C dV_C/dt and U_C = CV_C²/2. C is entered in µF, R in Ω, and the voltages in V. Allowed ranges are 0.01…50 µF, 100…50000 Ω and 0…100 V. This is an ideal lumped circuit with constant C and R, without leakage, lead inductance or propagation effects.

The solid wire-current curve and dashed displacement-current curve overlap: both expressions give the same signed current. Charging has positive current; discharge or a downward voltage step has negative current. At constant voltage both currents vanish, although charge and stored energy can remain. The interval ends at 6τ, where a finite transient still remains; the separate t → ∞ values show the limiting state.

What the sketch means

The left plate is positive when V_C > 0 and the electric field points toward the right plate. During discharge the field keeps this direction while its strength decreases; the current arrows reverse. The gap arrow represents displacement current, not charge carriers crossing the insulating gap. Arrow lengths and plate spacing are schematic and do not specify absolute electric or magnetic fields.

In the vacuum-gap picture, I_d = ε₀ dΦ_E/dt. A surface through the wire and a surface through the gap, sharing the same boundary, give consistent current and electric-flux-change terms. The complete flux matters. This sketch is not a field solution for arbitrary plate geometry or frequency; in materials, polarization must also be considered.

Example: C = 1 µF, R = 1000 Ω, 0 → 12 V gives τ = 1 ms. At t = τ, V_C ≈ 7.58545 V and both currents ≈ 4.41455 mA.

Sources

OpenStax, University Physics 2, §10.5: RC Circuits — charging, time constant and limiting behavior. The general initial voltage follows from the same linear RC equation with V_C(0) = V₀.
The Feynman Lectures on Physics, II §18.2 — displacement current and the capacitor gap.