# How do I know that ##i_x = 0## ?

• Engineering
In summary, the conversation discusses the concept of short-circuiting in a circuit with a 4-ohm resistor. The voltage across the 4-ohm resistor is zero, indicating that there is no current flowing through it. Despite being short-circuited, the resistance of the 4-ohm resistor remains the same and does not act as a short circuit.
Homework Statement
How do I know that ##i_x = 0 ~ ?## Is it because of the fact that resistor, source and dependent current source are in parallel? If that is not the reason, what is?

Relevant Equations
Norton's theorem
I was first thinking that i_x is zero because the 4 ohms resistor can be ignored because it is parallel with a short circuit, but I assumed that only the resistance is zero whilst i_x flows through and that is what'd make the voltage across 4-ohms resistor to be zero.

In figure 4.44(a), the voltage across the 4-ohm resistor is zero. Therefore, there is no current flowing through the 4-ohm resistor. The resistance of that 4-ohm resistor has not changed. It is simply short-circuited.

Ahaaa got it, thank you!
Just to make sure, So when I have a short circuit parallel to a resistor, the resistor will basically always stay intact, whilst the current will be zero on the other hand.

I was kind of confused, because we say the 4-ohms resistor is short-circuited from which I derive that it acts as a short circuit i.e. current can freely run through that branch(/resistor) which is basically not the case at all.

## 1. How do I know that ##i_x = 0## is true?

The value of ##i_x## can be determined by using mathematical equations and principles. If all the variables and constants in the equation are known, then the value of ##i_x## can be calculated. Once the calculation is done and the value of ##i_x## is found to be equal to 0, then it can be concluded that ##i_x = 0## is true.

## 2. Can I trust that ##i_x = 0## is accurate?

The accuracy of the statement ##i_x = 0## depends on the accuracy of the variables and constants used in the equation. If there are any errors or uncertainties in the values, then the accuracy of the statement may be affected. It is important to use reliable and accurate data in order to trust the accuracy of the statement.

## 3. How do I verify that ##i_x = 0## is correct?

The best way to verify the correctness of the statement ##i_x = 0## is by using the scientific method. This involves conducting experiments or observations to test the statement and see if it holds true. If the results consistently show that ##i_x = 0##, then it can be considered as correct.

## 4. What if the value of ##i_x## is not exactly 0?

In science, it is common to have values that are not exactly 0 due to limitations in measurement tools and human error. However, if the value of ##i_x## is very close to 0, it can still be considered as 0 for practical purposes. Scientists often use significant figures to indicate the precision and accuracy of a value.

## 5. Can the statement ##i_x = 0## change in the future?

In science, our understanding and knowledge are constantly evolving. This means that the statement ##i_x = 0## can potentially change in the future if new evidence or information is discovered. It is important to always question and re-evaluate our beliefs and theories in light of new data and advancements in science.

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