Question

Consider Figure 3.25 of the text for a transformer with off-nominal turns ratio.

(i) The per-unit equivalent circuit shown in part (c) contains an ideal transformer which cannot be accommodated by some computer programs.

(a) True

(b) False

(ii) In the- circuit representation for real c in part (d), the admittance parametersandwould be unequal.

(a) True

(b) False

(iii) For complex c, can the admittance parameters be synthesized with a passive RLC circuit?

(a) Yes

(b) No

Short answer

1. The correct option is (b) False.
2. The correct option is (a) True.
3. The correct option is (b) No.

Step-by-step solution

Determine the correct option for (i)

The part (c) of figure 3.25 is given below:

In the diagram, the turns ratio is$c$.

The secondary voltage reffered to primary side is given by,

$V_2=c{V}_1$ …… (1)

The secondary current reffered to primary side is given by,

$I_2=\frac{1}{c}{I}_1$ …… (2)

Using expressions (1) and (2), the equivalent circuit can be easily obtained which reffered to primary side.

So, using computer programs, the equivalent circuit can be solved.

Hence, the correct option is (b) false.

Determine the correct option for (ii)

(ii)

The part (d) of figure 3.25 is given below:

From the above diagrams, the admittances$Y_{11}$, $Y_{12}$, $Y_{21}$and$Y_{22}$ is written as;

$Y_{11}=Y_{eq}$ …… (3)

$Y_{12}=-c{Y}_{eq}$…… (4)

$Y_{21}=-c*Y_{eq}$…… (5)

$Y_{22}={\left|c\right|}^2{Y}_{eq}$…… (6)

Therefore, from equations (3) and (4), the admittances$Y_{11}$ and$Y_{12}$ would be unequal.

Hence, the correct option is (a) true.

Determine the correct option for (iii)

(iii)

From the equations (4) and (5), the admittances$Y_{21}$and $Y_{22}$ would be equal for real $c$.

But, the same admittances would be unequal for complex $c$.

Therefore, for complex $c$, the admittance parameters connot besynthesized with a passive RLC circuit

Hence, the correct option is (b) No.