91影视

Number of turns between taps is $N_{T1T2}=200$.

Number of turns between taps is $N_{T2T3}=800$.

Figure 31-37 is the transformer.

We use the concept of transformer. Using the equation of ratio of voltages related to ratio of number of turns, we can find the ratio of voltages.

a.

The smallest ratio when primary turns are larger than secondary; take $T_2{T}_3$as primary and $T_1{T}_3$as secondary and write the following formula.

$$\begin{gathered} \frac{V_s}{V_p}=\frac{V_{13}}{V_{23}} \\ =\frac{N_s}{N_p} \\ =\frac{\left(800+200\right)}{800} \\ =1.25 \end{gathered}$$

Hence, the smallest value of ratio $\frac{V_s}{V_p}$ for step-up transformer is 1.25.

b.

For the second smallest ratio, take $T_1{T}_2$as primary and $T_2{T}_3$as secondary, and define the ratio as follow.

$$\begin{gathered} \frac{V_{23}}{V_{12}}=\frac{800}{200} \\ =4.00 \end{gathered}$$

Hence, the second smallest value of ratio $\frac{V_s}{V_p}$for step-up transformer is 4.00.

c.

Largest value $\frac{V_s}{V_p}$for step-up transformer:

For largest ratio, take$T_1{T}_3$ as primary and $T_1{T}_3$as secondary, and define the ratio as below.

$$\begin{gathered} \frac{V_{13}}{V_{12}}=\frac{\left(800+200\right)}{200} \\ =5.00 \end{gathered}$$

Largest value of $\frac{V_s}{V_p}$ for step-up transformer 5.0.

d.

Exchange the primary and secondary values, so you obtain

$$\begin{gathered} \frac{V_{12}}{V_{13}}=\frac{1}{5.00} \\ =0.200 \end{gathered}$$

Thus, the smallest value of ratio $\frac{V_s}{V_p}$ for step-down transformer is 0.20.

e.

Second smallest value of $\frac{V_s}{V_p}$for step-down transformer:

$$\begin{gathered} \frac{V_{12}}{V_{23}}=\frac{1}{4.00} \\ =0.250 \end{gathered}$$

Second smallest value of ratio $\frac{V_s}{V_p}$ for step-down transformer is 0.250.

f.

Largest value of $\frac{V_s}{V_p}$for step-down transformer.

$$\begin{gathered} \frac{V_{23}}{V_{13}}=\frac{1}{1.25} \\ =0.800 \end{gathered}$$

Hence, the largest value of $\frac{V_s}{V_p}$ for step-up transformer is 0.800.