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To determine the voltage \( V_3 \) at \( t = 0^+ \) for the given circuit, we'll first analyze the circuit as depicted in the image.

### Key Points:
1. **Initial Condition at \( t = 0^- \):** 
   - Before \( t = 0 \), the circuit is in a steady state.
   - The inductor \( L \) behaves like a short circuit since DC current through it will have established a constant value.

2. **At \( t = 0^+ \):**
   - As the switch is opened or closed (depending on the circuit), the inductor will oppose any sudden changes in current due to its property of inductance. 
   - The current through the inductor just before \( t = 0 \) will be the same as just after \( t = 0 \).
   - The voltage across the inductor, \( V_L \), is initially determined by the current through it and any sudden change in voltage.

### Steps to Find \( V_3(t = 0^+) \):

1. **Determine the initial current through the inductor**:
   - If the circuit was in steady state before \( t = 0 \), calculate the current \( I_L \) using Ohm's Law and equivalent resistance in the circuit.

2. **Apply Kirchhoff's Voltage Law (KVL)**:
   - Apply KVL in the loop containing the inductor \( L \), resistor \( R_3 \), and the source \( V_s \) to express \( V_3 \) as a function of \( I_L \).

3. **Use the Inductor’s Voltage-Current Relationship**:
   - At \( t = 0^+ \), the voltage across the inductor can be written as \( V_L = L \frac{dI_L}{dt} \).

4. **Calculate \( V_3 \)**:
   - \( V_3(t = 0^+) \) is the voltage drop across \( R_3 \). Use the relation \( V_3(t = 0^+) = I_L(t = 0^+) \cdot R_3 \).

### Detailed Analysis:
Let me analyze the circuit in more detail and solve for \( V_3(t = 0^+) \).

- **Inductor at \( t = 0^- \)**:
  - Current \( I_L \) is steady-state and can be calculated considering \( R_1 \) and \( R_2 \) are in series and then in parallel with \( R_3 \).
  
- **Voltage across \( R_3 \) at \( t = 0^+ \)**:
  - The inductor will try to maintain the current at its pre-\( t = 0 \) value, thus we can find \( V_3(t = 0^+) \) using Ohm’s law with this current.

I'll proceed with this analysis, but please confirm if the circuit switch was just opened or closed at \( t = 0 \), as this impacts the initial condition.

Discover how to determine the voltage V3 at t=0+ in an electrical circuit with inductors and resistors. This problem involves applying Kirchhoff's Voltage Law and understanding the behavior of inductors in circuits. Suitable for advanced learners in circuit analysis.

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