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: Understanding the Question:
The question requires us to identify which of the components in the given series circuit are linear. A linear circuit element is one that obeys the principle of superposition and homogeneity. In simpler terms, its voltage-current (V-I) relationship can be described by a linear equation, resulting in a straight-line V-I characteristic graph that passes through the origin.
Step 2: Detailed Explanation:
Let's analyze the V-I relationship for each component:

• Resistor (R): An ideal resistor follows Ohm's Law, \(V = I \cdot R\). The voltage across the resistor is directly proportional to the current flowing through it. This is a linear relationship. Therefore, the resistor is a linear component.
• Inductor (L): The relationship for an ideal inductor is \(V = L \frac{di}{dt}\). The voltage is directly proportional to the rate of change of current. This is a linear differential relationship. Therefore, the inductor is a linear component.
• Capacitor (C): The relationship for an ideal capacitor is \(I = C \frac{dv}{dt}\). The current is directly proportional to the rate of change of voltage. This is also a linear differential relationship. Therefore, the capacitor is a linear component.
• Diode (D): The V-I relationship for a diode is described by the Shockley diode equation, which is exponential: \(I = I_s (e^{V_D / (n V_T)} - 1)\). Since the relationship between voltage and current is exponential and not a straight line, the diode is a non-linear component.

Step 3: Final Answer:
Based on the analysis, the resistor (R), inductor (L), and capacitor (C) are linear components, while the diode (D) is a non-linear component. Therefore, the correct option identifies only R, L, and C as linear.