# Finding the constraint equation of a circuit with a dependent voltage

• Engineering
• johnsmith7565
In summary, I am stuck on finding the constraint equation for i on the top question. I don't know how to find it when it's through a voltage source and not over any resistors. After I find i the problem should become easy to solve. I know that v1 = 10 and v2 = 20i. The KCL for v0 is (v0-10)/10 + v0/24 + (v0-20i)/20. I could write the KCL for v1 and v2 but that doesn't address how to find the constraint which is what I need. And when I write them and solve for my answer is way off. Something tells me I need a new approach.
BvU said:
My turn to be confused: if ##V_2=+64## V, the CCVS delivers ##-##64 V and pumps 3.8 A towards point V2. The ##-##64 is 20 times the ##-##3.2 A ##i_\Delta##.

If the CCVS sets ##V_2=+ 6.80851 ## V, the dial must read ##-6.80851 ## V which is minus 20 times the then ##-##0.34 A ##i_\Delta##.
Your first short paragraph above describes the situation as shown in the schematic of post #1.

The second short paragraph describes what would happen if the CCVS control law were changed from 20 IΔ to -20 IΔ, or if the orientation of the CCVS were flipped upside down with no change to the control law.

That's what Baluncore is referring to when he says "reverse the CCVS polarity".

Baluncore and BvU
<h2>What is a dependent voltage in a circuit?</h2><p>A dependent voltage in a circuit is a voltage that is not directly supplied by a voltage source, but rather is dependent on the values of other components in the circuit.</p><h2>Why is it important to find the constraint equation of a circuit with a dependent voltage?</h2><p>Finding the constraint equation allows us to accurately analyze the behavior of the circuit and determine the relationship between the dependent voltage and other components in the circuit.</p><h2>How do you find the constraint equation of a circuit with a dependent voltage?</h2><p>The constraint equation can be found by applying Kirchhoff's voltage law (KVL) and Ohm's law to the circuit, taking into account the dependent voltage and any other relevant components.</p><h2>Can the constraint equation change if the circuit components are altered?</h2><p>Yes, the constraint equation can change if the circuit components are altered. This is because the dependent voltage is affected by the values of other components in the circuit, so any changes to these values will also impact the constraint equation.</p><h2>How does the constraint equation affect the overall behavior of the circuit?</h2><p>The constraint equation helps to determine the overall behavior of the circuit by providing a relationship between the dependent voltage and other components. This allows us to predict and analyze the behavior of the circuit under different conditions.</p>

## What is a dependent voltage in a circuit?

A dependent voltage in a circuit is a voltage that is not directly supplied by a voltage source, but rather is dependent on the values of other components in the circuit.

## Why is it important to find the constraint equation of a circuit with a dependent voltage?

Finding the constraint equation allows us to accurately analyze the behavior of the circuit and determine the relationship between the dependent voltage and other components in the circuit.

## How do you find the constraint equation of a circuit with a dependent voltage?

The constraint equation can be found by applying Kirchhoff's voltage law (KVL) and Ohm's law to the circuit, taking into account the dependent voltage and any other relevant components.

## Can the constraint equation change if the circuit components are altered?

Yes, the constraint equation can change if the circuit components are altered. This is because the dependent voltage is affected by the values of other components in the circuit, so any changes to these values will also impact the constraint equation.

## How does the constraint equation affect the overall behavior of the circuit?

The constraint equation helps to determine the overall behavior of the circuit by providing a relationship between the dependent voltage and other components. This allows us to predict and analyze the behavior of the circuit under different conditions.

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