We introduce an inverse engineering approach to drive an RC circuit. This technique is implemented experimentally (1) to reach a stationary regime associated with a sinusoidal driving voltage in a very short amount of time, (2) to ensure a fast discharge of the capacitor, and (3) to guarantee a fast change from one stationary regime to another driven at different frequencies. This work can be used as a simple experimental project dedicated to the computer control of a voltage source. Besides the specific example addressed here, the proposed method provides an original use of simple linear differential equations to control the dynamical quantities of a physical system and has therefore a certain pedagogical value.

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The attractor in phase space is defined as the parametric representation in the (q, q̇) space of the forced solution, i.e., solution (5) without the decaying exponential term. It is thus the locus of points (q(t),q̇(t)), parametrized by time t, which yields an ellipse.

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In practice, the voltage step provides a limitation for tf, so the simple capacitor-resistor model that we are using here is valid for times larger than the circuit size over the speed of light (say 1 ns). Below this time scale, wave-like effects will play a role and a more elaborate circuit model is required.

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