17.\text{ A }15\text{ kVA, }1100\text{ V/}220\text{ V, single-phase two-winding transformer is configured as a }1.32\text{ kV/}1.1\text{ kV autotransformer.}

$$\begin{gathered} \text{What will be the rating of the autotransformer?} \\ \end{gathered}$$

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The correct option/answer is 90kVA.

Here is the step-by-step explanation and derivation to find the rating of the autotransformer:

1. Understand the parameters of the two-winding transformer:
Apparent power rating ($S_{\text{2w}}$) = 15 kVA = 15,000 VA
Primary winding voltage ($V_1$) = 1100 V
Secondary winding voltage ($V_2$) = 220 V

2. Identify the autotransformer configuration:
The transformer is reconfigured as an autotransformer with the following voltage ratings:
Higher voltage side ($V_{\text{H}}$) = 1.32 kV = 1320 V
Lower voltage side ($V_{\text{L}}$) = 1.1 kV = 1100 V

Notice that the higher voltage is the sum of the primary and secondary winding voltages of the two-winding transformer:
$1320\text{V}=1100\text{V}+220\text{V}$
This indicates a series-additive connection, where the 220 V winding serves as the series winding, and the 1100 V winding serves as the common winding.

3. Calculate the autotransformer power rating using the standard formula:
The apparent power rating of an autotransformer ($S_{\text{auto}}$) configured from a two-winding transformer is related to its two-winding rating ($S_{\text{2w}}$) by the formula:

$$S_{\text{auto}}=S_{\text{2w}}\times \left(\frac{V_{\text{H}}}{V_{\text{H}}-V_{\text{L}}}\right)$$

4. Substitute the given values into the formula:

$$S_{\text{auto}}=15\text{kVA}\times \left(\frac{1320}{1320-1100}\right)$$

$$S_{\text{auto}}=15\text{kVA}\times \left(\frac{1320}{220}\right)$$

$$S_{\text{auto}}=15\text{kVA}\times 6$$

$$S_{\text{auto}}=90\text{kVA}$$

Therefore, the rating of the autotransformer will be 90 kVA.