Determine the primary impedance ZP for the transformer circuit in Fig. 18-18.

Question

Determine the primary impedance [latex]Z_P[/latex] for the transformer circuit in Fig. 18-18.

Accepted Answer

Use Formula (18-10).[latex]Z_P=(\frac{N_P}{N_S})^2 imes Z_S [/latex]Since [latex]Z_S = R_L[/latex], we have

[latex]Z_P=(\frac{V_P}{N_S})^2 imes R_L[/latex]

[latex]=(\frac{4}{1} )^2 imes 8 \Omega[/latex]

[latex]= 16 imes 8 \Omega[/latex]

[latex]= 128 \Omega[/latex]

The value of 128 [latex]\Omega[/latex] obtained for[latex] Z_P[/latex] using Formula (18-10) [latex]Z_P=(\frac{N_P}{N_S})^2 imes Z_S [/latex] can be verified as follows.

[latex]V_S=\frac{N_S}{N_P} imes V_P[/latex]

[latex]= \frac{1}{4} imes 32 V[/latex]

=8 V

[latex]I_S=\frac{V_S}{R_L}[/latex]

[latex]=\frac{8 V}{8 \Omega}[/latex]

= 1 A

[latex]I_P= \frac{V_S}{V_P} imes I_S[/latex]

[latex]= \frac{8 V}{32 V} imes 1 A[/latex]

=0.25 A

And finally,

[latex]Z_P=\frac{V_P}{I_P} [/latex]

[latex]=\frac{32 V}{0.25 A}[/latex]

[latex]=128 \Omega[/latex]

Question 18.16: Determine the primary impedance ZP for the transformer circu...

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