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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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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