Resolved Problems about Magnetic Coupling

Problem 78-11 Source: Problem 13-8 - page 552 - IRWIN, David J. - Book: Análise de Circuitos em Engenharia - Ed. Pearson - 4ª edição - 2013.

Determine V_o in the circuit shown in Figure 78-11.1.

Solution of the Problem 78-11

With the procedure adopted until now of the currents entering the points, as shown Figure 78-11.1 , we can write the circuit equations. So:

(6 + j3 ) I₁ + j I₂ = 0

j I₁ + (12 + j6 ) I₂ = 24∠0°

Soon, we got a system of two equations with two unknowns. Solving the system with Octave, we find:

I₁ = -0.21 - j0.16 A

I₂ = 1.596 - j0.78 = 1.7764∠-26° A

To calculate the value of V_o we do the mesh equation on the secondary, or:

V_o = 24∠0° - 2 I₂ = 24∠0° - 2 x 1.7764∠-26°

Carrying out the calculation, we find:

V_o = 20.865∠4.29° V

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