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Dependent and Independent Sources

In circuit analysis, sources are the heart of any network. They provide the energy that drives current and creates voltage differences. This course explains the key concepts behind dependent…

10 questions~5 min
Dependent and Independent Sources — Qwi
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1

Which symbol correctly represents a voltage‑controlled current source (VCCS)?

2

If a dependent source follows the relation vn = 4 in, what type of source is it?

3

A 12 V battery is best classified as which of the following?

4

Which parameter has the unit siemens (S) in the context of dependent sources?

5

In a circuit, a dependent source whose output current is proportional to a controlling current is called:

6

Which of the following statements about independent sources is false?

7

A VCVS has the equation vn = μ vn. What does the symbol μ represent?

8

Which dependent source type is correctly matched with its controlling variable and output?

9

For a CCVS, the parameter r has which physical dimension?

10

Which of the following best explains why a dependent source is drawn with a diamond shape?

Understanding Dependent and Independent Sources

In circuit analysis, sources are the heart of any network. They provide the energy that drives current and creates voltage differences. This course explains the key concepts behind dependent (controlled) sources and independent sources, their symbols, classifications, and the parameters that define their behavior. Mastering these ideas will help you solve problems quickly, ace quizzes, and design reliable circuits.

1. Symbolic Representation of Dependent Sources

Every dependent source has a distinct schematic symbol that tells you two things:

  • What variable controls the source (voltage or current).
  • What quantity the source delivers (voltage or current).

The most common symbol you will encounter is the diamond shape. Inside the diamond, an arrow indicates the direction of the output quantity.

Key point: A diamond with a current arrow inside denotes a Voltage‑Controlled Current Source (VCCS). The diamond signals a dependent source, while the arrow shows that the output is a current.

2. Classifying Dependent Sources by Their Controlling Variable

Dependent sources are categorized by the type of controlling variable (voltage v or current i) and the type of output they produce. The four basic types are:

  • VCCS: Voltage‑controlled, current output.
  • VCVS: Voltage‑controlled, voltage output.
  • CCCS: Current‑controlled, current output.
  • CCVS: Current‑controlled, voltage output.

Each type follows a simple linear relationship. For example, a VCCS obeys iout = g·vcontrol, where g is the transconductance measured in siemens (S).

3. Real‑World Example: Identifying a Source from Its Equation

Consider the equation vn = 4·in. The output is a voltage (v) that depends on a controlling current (i). This matches the definition of a Current‑Controlled Voltage Source (CCVS). The constant “4” is the transresistance (r) expressed in ohms, linking current to voltage.

Remember: When the controlling variable is a current and the output is a voltage, you have a CCVS.

4. Independent Sources: Fixed vs. Variable

An independent source supplies a predetermined voltage or current regardless of other circuit elements. Batteries, ideal voltage generators, and current sources are classic examples.

  • They are represented by a circle (not a diamond).
  • Their value can be constant (e.g., a 12 V battery) or time‑varying (e.g., a sinusoidal voltage source).
  • They never depend on another circuit variable; their value is self‑driven.

Therefore, the statement “their value depends on another circuit variable” is false for independent sources.

5. Units and Parameters of Dependent Sources

Each dependent source type has an associated parameter that quantifies the relationship between the controlling variable and the output. Knowing the correct unit helps you identify the source type quickly.

  • Transconductance (g) – units: siemens (S). Used for VCCS (current output per volt input).
  • Transresistance (r) – units: ohms (Ω). Used for CCVS (voltage output per ampere input).
  • Current gain (β) – dimensionless. Used for CCCS (current output per ampere input).
  • Voltage gain (μ) – dimensionless. Used for VCVS (voltage output per volt input).

For instance, the parameter with unit siemens belongs to a VCCS, confirming that g is the correct answer when asked about the siemens unit.

6. Detailed Look at Each Dependent Source Type

6.1 Voltage‑Controlled Current Source (VCCS)

Equation: iout = g·vcontrol

  • Control: Voltage.
  • Output: Current.
  • Parameter: Transconductance (g) in siemens.

Typical symbol: Diamond with a current arrow.

6.2 Voltage‑Controlled Voltage Source (VCVS)

Equation: vout = μ·vcontrol

  • Control: Voltage.
  • Output: Voltage.
  • Parameter: Voltage gain (μ), dimensionless.

Symbol: Diamond with a voltage arrow (often a plus/minus sign).

6.3 Current‑Controlled Current Source (CCCS)

Equation: iout = β·icontrol

  • Control: Current.
  • Output: Current.
  • Parameter: Current gain (β), dimensionless.

Symbol: Diamond with a current arrow, but the controlling variable is a current.

6.4 Current‑Controlled Voltage Source (CCVS)

Equation: vout = r·icontrol

  • Control: Current.
  • Output: Voltage.
  • Parameter: Transresistance (r) in ohms.

Symbol: Diamond with a voltage arrow.

7. Frequently Asked Quiz Questions Explained

Below are the quiz items you may encounter, each paired with a concise explanation that reinforces the concepts above.

  • Symbol for VCCS: Diamond with a current arrow – indicates a voltage‑controlled source delivering current.
  • Equation vn = 4·in: CCVS – voltage output controlled by current.
  • 12 V battery classification: Independent voltage source – provides a fixed voltage without any controlling variable.
  • Unit siemens (S): Transconductance of a VCCS – relates voltage input to current output.
  • Current proportional to controlling current: CCCS – current‑controlled, current output.
  • False statement about independent sources: “Their value depends on another circuit variable.” Independent sources are self‑driven.
  • Symbol μ in VCVS equation: Dimensionless voltage gain – amplifies voltage without adding resistance.
  • Correct matching of type, control, and output: VCCS – controlled by voltage, outputs current.

8. Practical Tips for Identifying Sources in Schematics

When you open a circuit diagram, follow this quick checklist:

  1. Shape: Circle = independent; Diamond = dependent.
  2. Arrow direction: Arrow pointing out of the symbol indicates the output quantity (current or voltage).
  3. Label: Look for a parameter name (g, r, μ, β) next to the symbol; its unit tells you the source type.
  4. Equation: If the problem provides an equation, match the controlling variable (v or i) with the output variable to determine the source category.

Using this systematic approach reduces errors and speeds up analysis.

9. Summary of Key Concepts

  • Dependent sources are represented by diamonds; independent sources use circles.
  • Four dependent source types: VCCS, VCVS, CCCS, CCVS.
  • Parameters and units:
    • g (siemens) – VCCS.
    • μ (dimensionless) – VCVS.
    • β (dimensionless) – CCCS.
    • r (ohms) – CCVS.
  • Independent sources provide a fixed voltage or current and do not depend on other circuit variables.
  • Recognize source type quickly by examining the controlling variable and the output variable in the given equation.

10. Further Reading and Practice

To deepen your understanding, explore these resources:

  • All About Circuits – Dependent Sources
  • Electronics Tutorials – Dependent Sources
  • Practice problems in any standard Fundamentals of Electric Circuits textbook, focusing on sections about controlled sources.

By mastering the symbols, equations, and parameters outlined in this course, you will be equipped to tackle any problem involving dependent and independent sources with confidence.