Vs = 85Z30° V, R1 = 11 N, L1 = 16 mH, L2 = f=60 Hz. %3D

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**Transcription for Educational Purposes**

1. Let  
   \( V_s = 85 \angle 30^\circ \, \text{V}, \, R_1 = 11 \, \Omega, \, L_1 = 16 \, \text{mH}, \, L_2 = 18 \, \text{mH}, \, M = 12 \, \text{mH}, \, R_2 = 15 \, \Omega \)  
   \( f = 60 \, \text{Hz} \).

   in the circuit shown below.

   ![Circuit Diagram]

(a) Find \( Z_{L1}, Z_{L2}, Z_{M} \).

(b) Represent \( V_1 \) as a function of \( I_1, I_2 \), and represent \( V_2 \) as a function of \( I_1, I_2 \).

(c) Write a mesh equation for mesh 1 (left) and write a mesh equation for mesh 2 (right).

(d) Find \( I_1, I_2, V_1, V_2 \).

(e) Find the input impedance \( Z_{in} = V_s/I_1 \).

**Explanation of Diagram:**

The circuit consists of two loops:

- **Left Loop (Mesh 1):** Contains a voltage source \( V_s \), a resistor \( R_1 \), and an inductor \( L_1 \). Current \( I_1 \) is flowing through this loop.
- **Right Loop (Mesh 2):** Contains an inductor \( L_2 \), a mutual inductance \( M \), and a resistor \( R_2 \). Current \( I_2 \) is flowing through this loop.
- **Mutual Inductance (M):** Connects the two loops, influencing the voltage induced in each loop due to the other's current.
Transcribed Image Text:**Transcription for Educational Purposes** 1. Let \( V_s = 85 \angle 30^\circ \, \text{V}, \, R_1 = 11 \, \Omega, \, L_1 = 16 \, \text{mH}, \, L_2 = 18 \, \text{mH}, \, M = 12 \, \text{mH}, \, R_2 = 15 \, \Omega \) \( f = 60 \, \text{Hz} \). in the circuit shown below. ![Circuit Diagram] (a) Find \( Z_{L1}, Z_{L2}, Z_{M} \). (b) Represent \( V_1 \) as a function of \( I_1, I_2 \), and represent \( V_2 \) as a function of \( I_1, I_2 \). (c) Write a mesh equation for mesh 1 (left) and write a mesh equation for mesh 2 (right). (d) Find \( I_1, I_2, V_1, V_2 \). (e) Find the input impedance \( Z_{in} = V_s/I_1 \). **Explanation of Diagram:** The circuit consists of two loops: - **Left Loop (Mesh 1):** Contains a voltage source \( V_s \), a resistor \( R_1 \), and an inductor \( L_1 \). Current \( I_1 \) is flowing through this loop. - **Right Loop (Mesh 2):** Contains an inductor \( L_2 \), a mutual inductance \( M \), and a resistor \( R_2 \). Current \( I_2 \) is flowing through this loop. - **Mutual Inductance (M):** Connects the two loops, influencing the voltage induced in each loop due to the other's current.
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