Question

An autotransformer converts 200V to 100V supplying same load. Copper saving is

• A. 25%
• B. 50%
• C. 75%
• D. 100%

Hint:

The saving of copper in an autotransformer is directly proportional to the transformation ratio \(k\) (where \(k < 1\)).
The closer the transformation ratio \(k\) is to unity (1), the higher the copper saving and the more economical the autotransformer becomes.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the percentage of copper saved when using an autotransformer instead of a two-winding transformer to convert a voltage of 200 V to 100 V while supplying the same load.
Copper saving in an autotransformer is an important economic benefit compared to a conventional two-winding transformer.

Step 2: Key Formula or Approach:
Let the transformation ratio of the autotransformer be \(k\), defined as:
\[ k = \frac{V_2}{V_1} \]
where \(V_1\) is the primary (input) voltage and \(V_2\) is the secondary (output) voltage, with \(V_2 < V_1\).
The formula for the weight of copper in an autotransformer (\(W_{auto}\)) in terms of the weight of copper in a two-winding transformer (\(W_{tw}\)) is:
\[ W_{auto} = (1 - k) W_{tw} \]
Therefore, the saving in copper (\(W_{saving}\)) is:
\[ W_{saving} = W_{tw} - W_{auto} = k \cdot W_{tw} \] The percentage of copper saving is:
\[ \text{Percentage Copper Saving} = k \times 100\% \]

Step 3: Detailed Explanation:

• First, determine the primary voltage \(V_1 = 200\text{ V}\) and the secondary voltage \(V_2 = 100\text{ V}\).

• Compute the transformation ratio \(k\):
\[ k = \frac{V_2}{V_1} = \frac{100}{200} = 0.5 \]

• Substitute the value of \(k\) into the percentage copper saving formula:
\[ \text{Percentage Copper Saving} = 0.5 \times 100\% = 50\% \]

• This means that 50% of the copper weight is saved by using an autotransformer instead of a standard two-winding transformer for this specific voltage ratio.

Step 4: Final Answer:
The copper saving is 50%.