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Vs = 85Z30° V, R1 = 11 2, L1 = 16 mH, L2 = 18 mH, M = 12 mH, R2 = 15 2 f= 60 Hz. in the circuit shown below. R1 11 12 M + Vs V1 V2 R2 L1 L2 u

Vs = 85Z30° V, R1 = 11 2, L1 = 16 mH, L2 = 18 mH, M = 12 mH, R2 = 15 2 f= 60 Hz. in the circuit shown below. R1 11 12 M + Vs V1 V2 R2 L1 L2 u

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Problem Statement 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 Description - The circuit consists of two loops (left and right). - **Loop 1** (Left): - It contains a voltage source \( V_s \) and a resistor \( R_1 \). - An inductor \( L_1 \) is present with voltage \( V_1 \) across it. - Current \( I_1 \) flows in the loop in the clockwise direction. - **Loop 2** (Right): - There is a coupled inductor \( M \) between the two loops. - An inductor \( L_2 \) with a voltage \( V_2 \) across it is in the loop. - A resistor \( R_2 \) is in series with the inductor. - Current \( I_2 \) flows in the loop in the clockwise direction. ### Tasks (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 \( Z_{\text{in}} = V_s/I_1 \).
Transcribed Image Text:### Problem Statement 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 Description - The circuit consists of two loops (left and right). - **Loop 1** (Left): - It contains a voltage source \( V_s \) and a resistor \( R_1 \). - An inductor \( L_1 \) is present with voltage \( V_1 \) across it. - Current \( I_1 \) flows in the loop in the clockwise direction. - **Loop 2** (Right): - There is a coupled inductor \( M \) between the two loops. - An inductor \( L_2 \) with a voltage \( V_2 \) across it is in the loop. - A resistor \( R_2 \) is in series with the inductor. - Current \( I_2 \) flows in the loop in the clockwise direction. ### Tasks (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 \( Z_{\text{in}} = V_s/I_1 \).
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