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The circuit shown appears to be a multi-loop circuit with resistors and three voltage sources. To find the currents \(I_1\), \(I_2\), and \(I_3\), we will need to apply Kirchhoff's Voltage Law (KVL) for each loop and Kirchhoff's Current Law (KCL) at the junctions.

### Given values:
- \(R_1 = R_2 = R_3 = R_4 = 2 \, \Omega\)
- \(R_5 = 1 \, \Omega\)
- \(\varepsilon_1 = 6 \, \text{V}\), \(\varepsilon_2 = 8 \, \text{V}\), \(\varepsilon_3 = 10 \, \text{V}\)

### Step-by-step approach:

1. **Define the loops and currents:**
   - \(I_1\): Current through \(R_1\) and \(\varepsilon_1\).
   - \(I_2\): Current through \(R_2\), \(R_5\), and \(\varepsilon_2\).
   - \(I_3\): Current through \(R_3\), \(R_4\), and \(\varepsilon_3\).

2. **Apply Kirchhoff's Current Law (KCL):**
   At junction \(a\) and \(b\):
   \[
   I_1 = I_2 + I_3
   \]

3. **Apply Kirchhoff's Voltage Law (KVL) for each loop:**

   - **Loop 1 (left loop through \(R_1\), \(R_2\), and \(\varepsilon_1\)):**
     \[
     \varepsilon_1 - I_1 R_1 - I_2 R_2 = 0
     \]
     Substituting values:
     \[
     6 - 2I_1 - 2I_2 = 0 \quad \Rightarrow \quad 2I_1 + 2I_2 = 6 \quad \Rightarrow \quad I_1 + I_2 = 3 \, \text{(Equation 1)}
     \]

   - **Loop 2 (right loop through \(R_3\), \(R_4\), and \(\varepsilon_3\)):**
     \[
     \varepsilon_3 - I_3 R_3 - I_3 R_4 = 0
     \]
     Substituting values:
     \[
     10 - 2I_3 - 2I_3 = 0 \quad \Rightarrow \quad 4I_3 = 10 \quad \Rightarrow \quad I_3 = 2.5 \, \text{A} \, \text{(Equation 2)}
     \]

   - **Loop 3 (middle loop through \(R_2\), \(R_5\), and \(\varepsilon_2\)):**
     \[
     \varepsilon_2 - I_2 R_2 - I_3 R_5 = 0
     \]
     Substituting values:
     \[
     8 - 2I_2 - 1I_3 = 0 \quad \Rightarrow \quad 8 - 2I_2 - 2.5 = 0 \quad \Rightarrow \quad 2I_2 = 5.5 \quad \Rightarrow \quad I_2 = 2.75 \, \text{A} \, \text{(Equation 3)}
     \]

4. **Use KCL to find \(I_1\):**
   From KCL:
   \[
   I_1 = I_2 + I_3 = 2.75 + 2.5 = 5.25 \, \text{A}
   \]

### Final answer:
- \(I_1 = 5.25 \, \text{A}\)
- \(I_2 = 2.75 \, \text{A}\)
- \(I_3 = 2.5 \, \text{A}\)

Would you like more details on how the equations were formed or any other clarifications?

### Related Questions:
1. How does Kirchhoff's Current Law help in solving multi-loop circuits?
2. What happens if resistances are not equal in different loops?
3. Can we use mesh analysis for circuits with more than three loops?
4. How would the solution change if one of the batteries was reversed?
5. What other methods can be used to solve complex circuits like this one?

### Tip:
Always check the polarity of the voltage sources and the direction of current when applying Kirchhoff's Laws to ensure consistency in your equations.

Tentukan I1, I2, I3 jika R1 = 2 Ω, R2 = 2 Ω, R3 = 2 Ω, R4 = 2 Ω, R5 = 1 Ω, ε1 = 6 V, ε2 = 8 V, ε3 = 10 V.

Learn how to apply Kirchhoff's Voltage and Current Laws to solve for the currents I1, I2, and I3 in a complex multi-loop circuit with given resistances (R1 = 2 Ω, R2 = 2 Ω, R3 = 2 Ω, R4 = 2 Ω, R5 = 1 Ω) and voltage sources (ε1 = 6 V, ε2 = 8 V, ε3 = 10 V). Step-by-step analysis included.

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