A simple LC circuit with a parallel diode

An inductor in series or parallel with a capacitor is a well known electrical circuit that allows the voltage and current to oscillate sinusoidally with time. If a diode is inserted in parallel with the inductor, then the current in the inductor will remain approximately constant with time.


Introduction
An electrical circuit with an inductor provides a practical demonstration of Faraday's law, sometimes with surprising or unexpected consequences.A good example was published recently in this journal using a circuit with two inductors [1].An even simpler circuit is shown in figure 1 where a capacitor is discharged into an inductor with a diode in parallel with the inductor.
If the diode is omitted, the capacitor will discharge into the inductor when the switch is closed.The current in the inductor rises to a maximum value when the voltage across the capacitor decreases to zero, but since the current is a maximum at that time, the capacitor charges up again in the reverse direction.That is, the voltage across the capacitor changes sign.When the capacitor is fully charged in the reverse direction, the current Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
decreases to zero and the cycle starts again.In theory, the current will oscillate forever.In practice, the circuit eventually stops oscillating since the inductor will have a small resistance that gradually dissipates the energy initially stored in the capacitor.
If the diode is connected, then there is no immediate change when the switch is closed since no current can pass through a diode in the reverse direction.The capacitor therefore discharges through the inductor, as before, until the current is a maximum and the voltage across the capacitor decreases to zero.The current in the inductor does not suddenly decrease to zero at that time, but passes through the diode instead of charging the capacitor in the reverse direction.Ideally, the voltage across all three components would drop to zero at that time, and the current would continue to flow forever through the inductor and the diode in a closed loop.
In some applications, the current in the inductor can remain constant for months, provided the inductor is cooled with liquid helium and constructed from superconducting wire with zero R Cross Figure 1.LC circuit a diode in parallel with the inductor.
resistance.The diode also needs to be replaced with superconducting wire after the current reaches its maximum value.The main application is to provide a strong magnetic field inside the inductor, for experiments with particle accelerators or plasma physics experiments or in MRI instruments used in hospitals.
The circuit in figure 1 can still be used to generate large magnetic fields for various experiments without cooling the inductor.In that case, the inductor has a non-zero resistance, R, and the current, i, will decrease with time according to the relation assuming that the voltage drop across the diode is zero.The current is therefore given by i where i 0 is the maximum current.For example, if L = 1 mH and R = 0.1 Ω, then the current will decrease to e −1 i 0 = 0.368i 0 after a time t = L/R = 0.01 s.If the current needs to decrease over a longer time, then R needs to be reduced (using thicker wire) or L needs to be increased (using more turns).