The core of a three-phase, 50 Hz, 1000/400 V delta/star: 300 kVA core type transformer operated with a flux of 0.04 wb. Find the EMF per turn.
8.88 V
Transformer EMF per Turn Calculation
The question asks us to find the EMF per turn for a three-phase, core type transformer given its operating flux and frequency. The induced EMF in any winding of a transformer is related to the frequency of the supply, the maximum flux in the core, and the number of turns in that winding.
The fundamental formula for the induced EMF (RMS value) in a transformer winding is:
$$E = 4.44 \times f \times \Phi_m \times N$$
Where:
- $E$ is the RMS value of the induced EMF in volts.
- $f$ is the frequency of the supply voltage in Hertz (Hz).
- $\Phi_m$ is the maximum value of the flux in the core in Webers (Wb).
- $N$ is the number of turns in the winding.
We are asked to find the EMF per turn. This is simply the induced EMF divided by the number of turns, which can be derived from the formula above:
$$\text{EMF per turn} = \frac{E}{N} = 4.44 \times f \times \Phi_m$$
We are given the following values:
- Frequency, $f = 50$ Hz
- Maximum flux, $\Phi_m = 0.04$ Wb
Now, we can substitute these values into the formula for EMF per turn:
$$\text{EMF per turn} = 4.44 \times 50 \text{ Hz} \times 0.04 \text{ Wb}$$
Let's perform the calculation:
$$\text{EMF per turn} = 4.44 \times (50 \times 0.04)$$
$$\text{EMF per turn} = 4.44 \times 2.0$$
$$\text{EMF per turn} = 8.88 \text{ V}$$
So, the EMF induced per turn in the transformer winding is 8.88 Volts.
Let's compare this result with the given options:
- Option 1: 8.88 V
- Option 2: 5.5 V
- Option 3: 6 V
- Option 4: 11.2 V
Our calculated value, 8.88 V, matches Option 1.
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