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To solve the DC divider circuit shown in your image using mesh analysis, we need to identify the meshes and write the mesh equations based on the voltages around each loop.

### Circuit Description and Identification of Meshes:
The circuit has three essential meshes:
1. **Mesh 1** (left loop): Contains current \(i_1\) with resistors \(50\, \Omega\) and \(10\, \Omega\).
2. **Mesh 2** (middle loop): Contains current \(i_2\) with a voltage source (0.2V) and the current source (1A).
3. **Mesh 3** (right loop): Contains current \(i_3\) with resistors \(10\, \Omega\) and \(10\, \Omega\) and a dependent current source \(4i_4\).

### Writing Mesh Equations:
1. **Mesh 1**:
   \[
   150V - 50i_1 - 10(i_1 - i_4) = 0
   \]
   Simplifies to:
   \[
   60i_1 - 10i_4 = 150
   \]

2. **Mesh 2**:
   \[
   -0.2V + 10(i_2 - i_1) + 10(i_2 - i_3) = 0
   \]
   Simplifies to:
   \[
   20i_2 - 10i_1 - 10i_3 = 0.2
   \]

3. **Mesh 3**:
   \[
   10(i_3 - i_2) + 10i_3 + 1A = 0
   \]
   Since the current \(i_4\) from the dependent source \(4i_4\) is \(4i_4\), we have to find \(i_4\). Assuming \(i_4 = i_1\):
   \[
   20i_3 - 10i_2 = -1
   \]

### System of Equations:
The system of equations derived from the mesh currents is:
\[
\begin{align*}
60i_1 - 10i_4 & = 150, \\
20i_2 - 10i_1 - 10i_3 & = 0.2, \\
20i_3 - 10i_2 & = -1.
\end{align*}
\]
Substituting \(i_4 = i_1\), the final system of equations is:
\[
\begin{align*}
60i_1 - 10i_1 & = 150, \\
20i_2 - 10i_1 - 10i_3 & = 0.2, \\
20i_3 - 10i_2 & = -1.
\end{align*}
\]
We now solve these equations for \(i_1\), \(i_2\), and \(i_3\).

Let's calculate the currents.The solutions for the mesh currents are:
- \(i_1 = 3.00 \, \text{A}\)
- \(i_2 = 1.98 \, \text{A}\)
- \(i_3 = 0.94 \, \text{A}\)

Would you like more details or have any questions about how these values were calculated?

### Possible Next Questions:
1. How do the values of the currents affect the output voltage across the circuit?
2. What would happen if the value of the independent voltage source is changed?
3. How does the dependent current source \(4i_4\) impact the circuit behavior?
4. Could you explain why we assumed \(i_4 = i_1\) in the equations?
5. How would you modify the circuit to obtain a different output current?

### Tip:
When solving circuit equations, checking units consistency (like ensuring currents add up where junctions are involved) can help identify mistakes in the setup of equations.

Solve the DC divider circuit using mesh analysis to find i1, i2, i3, and i4 entirely by hand. Use substitution, Cramer's rule, or another method.

Learn how to solve a DC divider circuit using mesh analysis. This example demonstrates applying Kirchhoff's Voltage Law and Ohm's Law, with a dependent current source to find i1, i2, i3, and i4. Suitable for undergraduate electrical engineering students.

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