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To find the current through the \(1 \Omega\) resistor marked in red using nodal analysis, we will define the nodes and apply Kirchhoff's Current Law (KCL) to those nodes.

Here is the circuit broken down:
- Node V1 is the point between the \(3 \text{A}\) current source, \(2 \Omega\) resistor, and the \(1 \Omega\) resistor.
- Node V2 is the point between the \(1 \Omega\) resistor (where the red current arrow is), the \(5 \Omega\) resistor, and the \(1 \Omega\) resistor connected to the \(-2 \text{A}\) current source.

Let's assume the ground node is at the junction of the \(-2 \text{A}\) current source, \(1 \Omega\) resistor, and \(5 \Omega\) resistor.

### Nodal Equations
Using KCL, the sum of currents entering a node is zero. Assigning currents according to potential differences:

#### For Node V1:
- Current entering from the \(3 \text{A}\) source is \(3 \text{A}\).
- Current going to \(2 \Omega\) resistor: \(\frac{V1}{2}\).
- Current through \(1 \Omega\) resistor: \(\frac{V1 - V2}{1}\).

The equation for V1 is:
\[
3 - \frac{V1}{2} - \frac{V1 - V2}{1} = 0
\]

#### For Node V2:
- Current entering from the \(1 \Omega\) resistor: \(\frac{V1 - V2}{1}\).
- Current going to \(5 \Omega\) resistor: \(\frac{V2}{5}\).
- Current entering from the \(-2 \text{A}\) source is \(2 \text{A}\).

The equation for V2 is:
\[
\frac{V1 - V2}{1} - \frac{V2}{5} - 2 = 0
\]

We can now solve these two equations for \(V1\) and \(V2\), and then use the solution to find the current through the \(1 \Omega\) resistor.

Let's calculate it.

Please use Nodal analysis to find the current going through the 1 ohm resistor as indicated in red color in the provided circuit diagram.

Learn how to solve a circuit problem using nodal analysis to find the current through a 1 ohm resistor. This problem involves Kirchhoff's Current Law and requires solving two nodal equations. Suitable for undergraduate students in electrical engineering.

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