Final answer:
To determine the cross-sectional area of the transformer's core, the EMF equation for a transformer is utilized. The equation accounts for the number of turns, maximum magnetic flux, frequency, and EMF value. Based on the provided data, a calculation is made, revealing a discrepancy with the provided answer, indicating a potential error in the question details.
Step-by-step explanation:
The original question seeks to determine the cross-sectional area of the core in a transformer. To find the cross-sectional area of the core, using the EMF equation for a transformer, we have:
EMF = (N × Φ_max × A × f) / (√2)
where:
- N is the number of turns in the coil,
- Φ_max is the maximum magnetic flux,
- A is the cross-sectional area,
- f is the frequency of the alternating current,
- √2 is the square root of 2, accounting for the RMS value of EMF and the max value of flux.
Given values are:
- Φ_max = 0.1 Wb/m²,
- f = 50 Hz,
- N = 1000 turns,
- EMF = 222 V.
Re-arranging the formula to solve for A:
A = EMF × √2 / (N × Φ_max × f)
Substituting the given values:
A = 222 V × √2 / (1000 turns × 0.1 Wb/m² × 50 Hz)
Upon calculating, we find that the cross-sectional area, A, is approximately 0.0063 m², which is evidently not consistent with the provided answer choice of 22.2 m², suggesting there may be a typo or an error in the question details or assumptions.