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To solve this circuit using **Kirchhoff's Laws**, we will apply both Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).

### 1. **Label the currents:**
   - \( I_1 \): Current through the 20 Ω resistor.
   - \( I_2 \): Current through the 10 Ω resistor (vertical).
   - \( I_3 \): Current through the 10 Ω and 15 Ω resistors in the right branch.

### 2. **Kirchhoff's Current Law (KCL) at junction \( Q \):**
   According to KCL, the sum of currents entering a junction is equal to the sum of currents leaving the junction.
   \[
   I_1 = I_2 + I_3
   \]

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

#### Loop 1 (left loop: 80V, 20Ω, and 10Ω vertical resistor):
- Apply KVL around the left loop:
  \[
  80V - I_1 \cdot 20Ω - I_2 \cdot 10Ω = 0
  \]
  Simplifying this:
  \[
  80 = 20I_1 + 10I_2 \quad \text{(Equation 1)}
  \]

#### Loop 2 (right loop: 10Ω horizontal resistor, 15Ω, 90V):
- Apply KVL around the right loop:
  \[
  90V - I_3 \cdot 15Ω - I_3 \cdot 10Ω = 0
  \]
  Simplifying this:
  \[
  90 = 25I_3 \quad \text{(Equation 2)}
  \]
  Solving for \( I_3 \):
  \[
  I_3 = \frac{90}{25} = 3.6 \, A
  \]

### 4. **Substitute \( I_3 \) into the KCL equation:**
From KCL: 
\[
I_1 = I_2 + 3.6
\]
We can substitute this into Equation 1:
\[
80 = 20(I_2 + 3.6) + 10I_2
\]
Simplifying:
\[
80 = 20I_2 + 72 + 10I_2
\]
\[
80 = 30I_2 + 72
\]
\[
30I_2 = 8
\]
\[
I_2 = \frac{8}{30} = 0.267 \, A
\]

### 5. **Find \( I_1 \):**
Now that we have \( I_2 \), substitute it into the equation \( I_1 = I_2 + 3.6 \):
\[
I_1 = 0.267 + 3.6 = 3.867 \, A
\]

### Final Answer:
- \( I_1 = 3.867 \, A \)
- \( I_2 = 0.267 \, A \)
- \( I_3 = 3.6 \, A \)

Would you like further clarification or more details? 

Here are 5 related questions:
1. How does Kirchhoff's Voltage Law apply in more complex circuits?
2. Can Kirchhoff's laws be used for non-linear circuits?
3. What is the significance of the direction of currents in Kirchhoff’s laws?
4. How does solving using Kirchhoff’s laws compare with using Thevenin's theorem?
5. How can we verify the solution through simulation tools like SPICE?

**Tip:** When applying Kirchhoff's laws, always double-check the direction of currents and voltage drops to avoid sign errors.

Apply Kirchhoff’s laws, find the currents in the given circuit with 80V, 90V power supplies, and resistors of 20Ω, 10Ω, and 15Ω.

Learn how to apply Kirchhoff’s Current and Voltage Laws to solve a circuit with two power supplies (80V and 90V) and multiple resistors. This step-by-step guide will walk you through the process of calculating the currents I1, I2, and I3 using KCL and KVL.

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