Question

The EMF induced in the secondary winding of a 50 Hz single-phase transformer having 1000 turns on its secondary is 222 V. The maximum flux density in the core is 0.1 Wb/m². The cross-sectional area of the core is:

(a) 222 m²
(b) 111 m²
(c) 44.4 m²
(d) 22.2 m²

Answer 1

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.