Question

In the series circuit shown containing a voltage source (V), a diode (D), a resistor (R), an inductor (L), and a capacitor (C), which of the following components are considered linear?

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

Hint:

A simple rule of thumb for basic circuit elements is that the standard passive components—resistors (R), inductors (L), and capacitors (C)—are treated as linear. Semiconductor devices like diodes, transistors, and SCRs are inherently non-linear.

Answer 1

The Correct Option is D

Step 1: Definition of Linearity
A circuit component is linear if it satisfies two properties: Homogeneity (scaling) and Additivity (superposition). Mathematically, the relation between current (\(I\)) and voltage (\(V\)) must be a linear differential equation.
Step 2: Component Breakdown

• Resistor (R): \(V = IR\). This is a linear algebraic relationship.
• Inductor (L): \(V = L \frac{di}{dt}\). This is a linear differential relationship.
• Capacitor (C): \(I = C \frac{dv}{dt}\). This is also a linear differential relationship.
• Diode (D): \(I = I_s (e^{V/nV_T} - 1)\). The exponential term makes the relationship non-linear.

Step 3: Conclusion
Since R, L, and C are described by linear equations and the diode is described by a non-linear exponential equation, only R, L, and C are linear components.