Question

A circuit with ideal elements is shown.

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?

• A. R only
• B. R, L, and C only
• C. D only
• D. L, C, and D only

Hint:

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.

Answer 1

The Correct Option is B

Step 1: Recall what makes a circuit element linear.
An element is linear when its voltage-current relationship is proportional (or a constant-coefficient derivative/integral relation), so that scaling the current scales the voltage by the same factor, and the response to a sum of currents is the sum of the individual responses.
Step 2: Check the resistor.
\[ v_R=iR \]
a direct proportionality with constant \(R\), a textbook linear relation.
Step 3: Check the inductor.
\[ v_L=L\frac{di}{dt} \]
a linear differential relation with constant coefficient \(L\).
Step 4: Check the capacitor.
\[ i_C=C\frac{dv_C}{dt} \]
similarly linear, with constant coefficient \(C\).
Step 5: Check the diode.
An ideal diode is a switching element: it behaves like a short circuit (zero voltage drop) when forward biased and carrying current, and like an open circuit (zero current) when reverse biased, with an abrupt change of behavior at zero current/zero voltage. This piecewise, non-proportional switching behavior is fundamentally NONLINEAR; a diode never obeys a single constant-coefficient equation valid for all currents and voltages.
Step 6: Evaluate the options.
Option (A), R only, misses that L and C are also linear. Option (B), R, L, and C only, correctly includes all three passive linear elements and excludes the diode. Option (C), D only, is the opposite of the correct answer, since D is the one nonlinear element. Option (D), L, C, and D, wrongly includes the diode among the linear elements.
Step 7: Final Answer.
\[ \boxed{\text{R, L, and C only}} \]