If the same transformer in Question 1 is connected as an autotransformer, there will be four different possible autotransformer configurations. Assume that the input voltage is 600 V AC. Be sure to show ALL work. (12) a) What would be the four available output voltages using different connections?
The Correct Answer and Explanation is:
To solve this problem, we need to understand how an autotransformer works and how it can be configured using the same winding elements as a standard two-winding transformer.
Given:
Input voltage (primary voltage) = 600 V AC
This refers to a transformer in a previous question, which is not provided. So, we assume a typical step-down or step-up transformer with a primary voltage of 600 V and a secondary voltage of 240 V, a common transformer rating.
Step 1: Determine Turn Ratios
Let:
Vp = 600 V (primary voltage)
Vs = 240 V (secondary voltage)
Then:
The voltage ratio is 600 / 240 = 2.5
Now, when connected as an autotransformer, the primary and secondary windings are electrically connected, so the voltage combinations can be additive or subtractive.
Step 2: Determine the Four Autotransformer Configurations
Step-Up Configuration (Additive)
Total output voltage = Vp + Vs = 600 V + 240 V = 840 V
Step-Down Configuration (Using only secondary)
Output voltage = 240 V
Step-Down Configuration (Subtractive connection)
Total output voltage = Vp – Vs = 600 V – 240 V = 360 V
Step-Down Configuration (Tapping at the winding junction)
Input = 600 V
Tap between winding to give partial output:
Output voltage = (240 / 600) × 600 V = 240 V
Output voltage = (240 / 600) × 600 V = another 360 V, based on winding connections
However, in autotransformer design, we usually get four distinct output voltages when using both additive and subtractive combinations, plus tap points:
Final Answer:
The four available output voltages using different autotransformer connections are:
840 V (additive: 600 V + 240 V)
600 V (full winding: input voltage)
360 V (subtractive: 600 V – 240 V)
240 V (tap at secondary)
Explanation (around 300 words):
An autotransformer uses a single continuous winding that acts as both the primary and the secondary winding, with a portion of the winding common to both. Unlike a two-winding transformer, the autotransformer’s windings are physically connected, allowing different voltage outputs depending on where connections are made.
In this problem, the original transformer had a 600 V primary and 240 V secondary. When reconfigured as an autotransformer, this allows several possible voltage outputs depending on how the windings are tapped.
The first configuration is additive, where the secondary winding voltage is added to the primary, yielding a higher output of 840 V. This is useful in step-up applications.
The second is subtractive, where the secondary winding opposes the primary. The result is 360 V, which can be used where a reduced voltage is needed from a higher voltage source.
The third is simply tapping across the full input voltage, giving 600 V, which is useful if the load requires the same voltage as the supply.
The fourth configuration is tapping directly across the secondary portion of the winding, providing 240 V. This is equivalent to the original secondary voltage.
Each of these configurations offers flexibility in applications such as voltage regulation, motor starting, and variable voltage supplies, making autotransformers more versatile and efficient than traditional transformers in certain use cases.
