How Do You Analyze a Circuit with a Dependent Voltage Source?

In summary, the circuit shown in the figure has a dependent voltage source on the right which is related to the left part of the circuit through the voltage across the 2Ω resistor. The wire joining the two sections serves as a common reference node and the two parts are isolated from each other except for the dependent source mechanism. This type of source is known as a voltage controlled voltage source and there are four main types of dependent sources based on input and output characteristics.
  • #1
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Homework Statement



We have the circuit in the figure. http://oi40.tinypic.com/30kgl78.jpg.I have to find i and v1.

Homework Equations




Current division,KCL.KVL.

The Attempt at a Solution


I haven't seen any circuit like this. How to relate the left part of the circuit with the right one?
 
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  • #2
The left and right parts of the circuit are related through the dependent voltage source in the right. Imagine that there's a mechanism in place which measures v1 across the 2Ω resistor and sets the value of the voltage source accordingly.

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No current can flow if there isn't a closed circuit (loop). So the wire joining the two circuit sections only provides a common reference node. So other than the dependent source mechanism, the two parts of the circuit are effectively isolated from each other.
 

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  • #3
What gneil said.

The diamond on the right is a "dependant voltage source". It's voltage is dependant on the voltage (Vi) across the 2 Ohm resistor. In this case it has a gain of 4 meaning that it's output voltage is 4 * Vi. I suppose it's proper name would be a "Voltage controlled voltage source". In the real world this might be something like an amplifier. They also produce an output voltage that depends on the input voltage.

There are four main types of dependant source depending on the characteristics of the input and output..

Voltage controlled voltage source
Voltage controlled current source
Current controlled voltage source
Current controlled current source
 

FAQ: How Do You Analyze a Circuit with a Dependent Voltage Source?

What is circuit analysis?

Circuit analysis is the process of studying and understanding electrical circuits, which are systems that allow the flow of electrical current. This involves analyzing the behavior and interactions of various components, such as resistors, capacitors, and inductors, in order to determine the voltage, current, and power in the circuit.

Why is circuit analysis important?

Circuit analysis is important because it allows us to design and troubleshoot electrical circuits. It helps us understand how different components work together and how changes in one part of the circuit affect the rest of the system. This is essential for creating safe and efficient circuits.

What are the different methods of circuit analysis?

There are two main methods of circuit analysis: nodal analysis and mesh analysis. Nodal analysis involves using Kirchhoff's Current Law to analyze the voltage at different nodes in the circuit. Mesh analysis uses Kirchhoff's Voltage Law to analyze the current in different loops of the circuit. Both methods are equally valid and can be used to solve complex circuits.

How do I solve a circuit analysis problem?

To solve a circuit analysis problem, you will need to follow a systematic approach. This involves using the laws and principles of circuit analysis, such as Kirchhoff's Laws and Ohm's Law, to create equations and solve for the unknown values. It is important to label all components and use the correct units in your calculations.

What are the common mistakes in circuit analysis?

Some common mistakes in circuit analysis include forgetting to account for direction of current flow, not considering voltage drops across all components, and mixing up units in calculations. It is also important to double check any assumptions made and to ensure all values used are accurate. It can be helpful to practice and review your work to avoid these mistakes.

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