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To solve this circuit problem, we need to find the current \( I \) and the voltage across the resistor \( V_R \) using Kirchhoff's laws or the superposition theorem. Given that \( C_1 = 27 \), we can analyze the circuit step-by-step:

### Step 1: Circuit Simplification Using Impedances
1. The sources \( V_1 \) and \( V_2 \) are represented as sinusoidal voltages with \( C_1 \sqrt{2} \). Since \( C_1 = 27 \), the voltage sources are \( 27\sqrt{2} \) V.
   
2. Convert the inductors and capacitors to their impedances at 60 Hz:
   - Inductive reactance: \( X_L = j\omega L \) where \( j50 \) and \( j60 \) are already given impedances for the inductors.
   - Capacitive reactance: \( X_C = -j \frac{1}{\omega C} \). The given capacitive impedances are \( -j30 \) and \( -j20 \).

### Step 2: Applying Superposition Theorem
We solve the circuit twice, once with \( V_1 \) active and \( V_2 \) turned off (shorted), and once with \( V_2 \) active and \( V_1 \) turned off.

#### Case 1: \( V_1 \) Active, \( V_2 \) Shorted
1. Simplify the circuit by shorting \( V_2 \).
2. Calculate the total impedance seen by \( V_1 \).
3. Use Ohm's law to find the current \( I_1 \).

#### Case 2: \( V_2 \) Active, \( V_1 \) Shorted
1. Simplify the circuit by shorting \( V_1 \).
2. Calculate the total impedance seen by \( V_2 \).
3. Use Ohm's law to find the current \( I_2 \).

### Step 3: Superimpose Currents
- Total current \( I = I_1 + I_2 \).

### Step 4: Find the Voltage Across Resistor \( V_R \)
- Use \( V_R = I \times 100 \) ohms.

Would you like me to perform the calculations for each step in detail? 

Here are related questions you might explore:
1. How do you calculate the impedance of capacitors and inductors at different frequencies?
2. What is the significance of using the superposition theorem in circuit analysis?
3. How do Kirchhoff's laws apply to complex AC circuits?
4. How can you verify your solution using simulation software like SPICE?
5. What are the key differences in analyzing AC vs. DC circuits?

**Tip:** Always double-check impedance values, especially the signs, as they indicate whether the element is inductive (positive imaginary) or capacitive (negative imaginary).

Para o circuito visto na Fig. 3, calcular a corrente (I) e a tensão do resistor (V_R) assinalados. Utilizar as leis de Kirchhoff e/ou o teorema de superposição para resolver o circuito.

Learn how to analyze an AC circuit using Kirchhoff's laws and the superposition theorem to calculate the current (I) and voltage across the resistor (V_R). This problem covers AC circuit analysis, including complex impedance and phasor analysis, suitable for undergraduate electrical engineering students.

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