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

[Questions999]

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?

 

[gneill]

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.

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.

 

[CWatters]

What gneil said.

The diamond on the right is a "dependent voltage source". It's voltage is dependent 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 dependent 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