1 iin (t) Vin (t) ~ R₁ www Vout(t)- L₁ m C₁ For the above circuit, assume the following: Vin(t) = 15 cos(120πt +30°)V, R₁ = 5k, L₁ = 10mH, and C₁ = 5µF: A) Find the current Iin in Aiin 20in form in units of [mA]4[°]. B) Find the power factor of the voltage source (no units). C) Find the average (real) power P provided by the voltage source in units of mW. D) Find the reactive power Q provided by the voltage source in units of mV AR. E) Determine which kind of filter (Lowpass, Highpass, Bandpass, Notch) is the above circuit.

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**Problem Description:**

Consider the RL circuit shown. Assume the following parameters:
- Input voltage: \( v_{in}(t) = 15 \cos(120\pi t + 30^\circ) \) V
- Resistor \( R_1 = 5 \, k\Omega \)
- Inductor \( L_1 = 10 \, mH \)
- Capacitor \( C_1 = 5 \, \mu F \)

**Questions:**

A) Find the current \( I_{in} \) in \( A_{in} \angle \theta_{in} \) form in units of \([mA] \angle [^\circ]\).

B) Determine the power factor of the voltage source (unitless).

C) Calculate the average (real) power \( P \) provided by the voltage source in units of \( mW \).

D) Calculate the reactive power \( Q \) provided by the voltage source in units of \( mVAR \).

E) Identify the kind of filter (Lowpass, Highpass, Bandpass, Notch) represented by the circuit above.

**Diagram Explanation:**

The circuit diagram includes:
1. An AC voltage source denoted by \( v_{in}(t) \).
2. A resistor \( R_1 \).
3. An inductor \( L_1 \).
4. A capacitor \( C_1 \).

The components are connected in series, with the output voltage \( v_{out}(t) \) measured across the inductor and capacitor. The current \( i_{in}(t) \) flows through the circuit.
Transcribed Image Text:**Problem Description:** Consider the RL circuit shown. Assume the following parameters: - Input voltage: \( v_{in}(t) = 15 \cos(120\pi t + 30^\circ) \) V - Resistor \( R_1 = 5 \, k\Omega \) - Inductor \( L_1 = 10 \, mH \) - Capacitor \( C_1 = 5 \, \mu F \) **Questions:** A) Find the current \( I_{in} \) in \( A_{in} \angle \theta_{in} \) form in units of \([mA] \angle [^\circ]\). B) Determine the power factor of the voltage source (unitless). C) Calculate the average (real) power \( P \) provided by the voltage source in units of \( mW \). D) Calculate the reactive power \( Q \) provided by the voltage source in units of \( mVAR \). E) Identify the kind of filter (Lowpass, Highpass, Bandpass, Notch) represented by the circuit above. **Diagram Explanation:** The circuit diagram includes: 1. An AC voltage source denoted by \( v_{in}(t) \). 2. A resistor \( R_1 \). 3. An inductor \( L_1 \). 4. A capacitor \( C_1 \). The components are connected in series, with the output voltage \( v_{out}(t) \) measured across the inductor and capacitor. The current \( i_{in}(t) \) flows through the circuit.
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