Lab 3 - Ideal Transformers

Lab 3 - Ideal Transformers

Prelab (none)

Problem

To investigate the concept of mutual inductance and how it is applied in a transformer.

Introduction

Your introduction should mention:

What an ideal transformer is and the governing equations related to this lab session.
- How Voltage, Current, and Power are related between the two windings in the transformer.
- What the "center-tap" is on the transformer.
Which assumptions and behaviors would change if this were not an ideal transformer.
What is meant by mutual inductance?

Equipment & Components

1x Isolation transformer

1x AC Autotransformer (as AC source)

1x 1 kVA single-phase transformer (1 per 2 groups)

1x 13.5Ω variable resistor (rheostat)

4x Multimeters

Circuit 2.1

Procedure

Part 1: Dot Convention

Verify that the dot marking is indicated at the expected position.
- Apply a small voltage ~10V to one of the windings.
- Measure voltage V' at the center tap as shown.

Part 2: Coupling Coefficient

Measure the resistance of the two windings shown in Circuit 2.1.
These losses are not accounted for in the behavior of an ideal transformer.
The mutual inductance of a transformer can be found as follows:

Circuit 2.2

Only V_testV_coil & I_coil are test paramters, you will calculate X in the results section.

Important Notes:

The flux in the core must be constant. The core flux can be determined by observing the voltage induced in the third coil. Adjust the supply between tests such that 49V is read across the 3^rd coil at all times.

To avoid blowing fuses in the ammeters, turn the applied voltage down to zero after each test, and slowly increase the voltage to V_test.

Part 3: Transformer Action

Connect the transformer as shown in Circuit 2.2.
Apply 120V_AC to the primary.
Measure all voltages and currents.
- Use the "A" range for the current measurements.

Results

Part 1: Dot Convention

Verify the dot marking of the transformer. (note that the dots in the circuit shown are arbitrary)
- If V' is greater than V, the dot should be placed on (b).
- If V is greater than V' the dot should be placed on (a).

Part 2: Mutual Inductance

Show the results for the chart given above.
Determine the mutual inductance X_M and coupling coefficient k:
- Adding X_T = X₁ + X₂ + 2X_M
- Opposing X_T = X₁ + X₂ – 2X_M
- Solve for X_M in each, and average for use below. If your X_M values are not close, there may have been a measurement error.
- Using the above two equations: k = X_M / √( X₁X₂).
- What does the k value imply ?

Part 3: Transformer Action

Create a chart showing the Voltage, Current, Power, and Impedance on the primary and seconday.
Do the current and voltage ratios agree with theory?
- Does the power on the primary equal the power on the secondary?
Is this an ideal transformer?
What impedance is presented to the source? Is this what you would expect?

Questions

Where else do losses occur in transformers, aside from the resistance in the windings?
- How can these losses be mitigated?
Knowing the function of the center-tap, why might it be useful?
As configured in Circuit 2.2, what is the behavior of the transformer?
Why is it important to maintain the core flux when testing the transformer?

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