Question

Explain the passive sign convention for resistors, capacitors, and inductors.

Answer 1

The passive sign convention is a widely used convention in electrical engineering to define the polarity and direction of voltage, current, and power in circuit elements such as resistors, capacitors, and inductors. This convention helps maintain consistency and clarity when analyzing and designing electrical circuits.

Resistors:
For resistors, the passive sign convention states that the current through the resistor flows from the higher potential (voltage) terminal to the lower potential terminal. In other words, the positive terminal of the resistor is where the current enters, and the negative terminal is where it exits. The voltage drop across a resistor is considered positive when the current enters the positive terminal and negative when it enters the negative terminal.

Capacitors:
For capacitors, the passive sign convention is based on the change in voltage across the capacitor and the direction of the current flow. When a capacitor is charging, the current flows into the positive terminal of the capacitor. The voltage across the capacitor is considered positive when the voltage at the positive terminal is higher than at the negative terminal. During discharge, the current flows out of the positive terminal, and the voltage across the capacitor is considered negative when the voltage at the positive terminal is lower than at the negative terminal.

Inductors:
For inductors, the passive sign convention is also based on the direction of current flow and the resulting voltage polarity. When the current through an inductor increases, the voltage across it is considered positive at the terminal where the current enters and negative at the terminal where it exits. Conversely, when the current decreases, the voltage across the inductor is considered negative at the terminal where the current enters and positive at the terminal where it exits.

In summary, the passive sign convention is a consistent way to define the positive and negative polarity of voltage, current, and power for resistors, capacitors, and inductors, making circuit analysis and design more straightforward and standardized.

Answer 2

The Passive Sign Convention is a set of rules used in electrical engineering to define the positive direction of current and voltage for passive components, such as resistors, capacitors, and inductors, in circuit analysis. The convention provides a consistent way to interpret the polarity and direction of voltage and current in passive components.

Resistors:

For a resistor, the passive sign convention states that the current flows from the positive terminal to the negative terminal.
The voltage drop across a resistor is considered positive when the current enters the positive terminal and exits through the negative terminal.
The power dissipated by a resistor is positive when the current flows from the higher potential to the lower potential.

Capacitors:

For a capacitor, the passive sign convention defines the voltage across the capacitor and the direction of the current through it.
The voltage across the capacitor is considered positive when the positive terminal has a higher potential than the negative terminal.
The current through the capacitor is positive when it flows from the positive to the negative terminal of the capacitor.
During charging (when the capacitor is storing energy), the current flows from the positive to the negative terminal, and the voltage across the capacitor increases.
During discharging (when the capacitor is releasing energy), the current flows from the positive to the negative terminal, and the voltage across the capacitor decreases.

Inductors:

For an inductor, the passive sign convention determines the polarity of the voltage across the inductor and the direction of the current passing through it.
The voltage across the inductor is considered positive when the positive terminal has a higher potential than the negative terminal.
The current through the inductor is positive when it flows from the negative to the positive terminal of the inductor.
When the current through the inductor increases, the magnetic field around the inductor grows, resulting in a voltage drop across the inductor that opposes the change in current (inductive kickback).
When the current through the inductor decreases, the magnetic field collapses, resulting in a voltage drop across the inductor that again opposes the change in current.

Remember that the Passive Sign Convention is just a convention used for consistency in circuit analysis and calculations. Engineers use it to ensure that their calculations and interpretations of circuit behavior align with the standard principles of circuit theory.