The circuit has a DC source \(V_{DC}\) in series with an ideal diode \(D\), a resistor \(R\), an inductor \(L\), and a capacitor \(C\) (the capacitor is connected across the series combination of \(L\) at the far end of the loop).
Which one of the following options correctly identifies all the linear elements in the circuit?
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Resistors, inductors, and capacitors all have constant-coefficient proportional v-i relationships; an ideal diode's on/off switching behavior is not proportional and is nonlinear.
A quick way to settle this is to recall that R, L, and C are always grouped together as the three canonical passive linear elements taught at the start of any circuits course, and to treat every semiconductor device as suspect until checked.
The defining equations of the resistor, inductor, and capacitor,
are each a constant multiplied by a variable or its derivative, the signature of linearity: doubling the current doubles the voltage (or vice versa) in every case, with no thresholds and no piecewise breaks.
The diode, on the other hand, conducts current in only one direction and blocks it in the other, an inherently switching, non-proportional behavior. Even the ideal (zero forward-drop) diode model used here is nonlinear, since it still has two completely different regimes (short circuit versus open circuit) depending on the sign of the current or voltage, which no single linear equation can capture.
So among the four elements shown, only R, L, and C are linear.
