Question

Transformers are often rated in terms of kilovolt-amps. A pole on a residential street has a transformer rated at $35 \mathrm{kV} \cdot \mathrm{A}$ to serve four homes on the strect. (a) If each home has a fuse that limits the incoming current to \(60 \mathrm{A}\) rms at \(220 \mathrm{V}\) rms, find the maximum load in \(\mathrm{kV} \cdot \mathrm{A}\) on the transformer. (b) Is the rating of the transformer adequate? (c) Explain why the transformer rating is given in kV.A rather than in kW.

Short answer

Also, explain why the transformer rating is given in kVA rather than kW. #Answer: The maximum load on the transformer is approximately 52.8kVA. The transformer's rating of 35kVA is NOT adequate to handle the load, as 52.8kVA exceeds the 35kVA rating. Transformer ratings are given in kVA because transformers deal with voltages and currents, not power directly. Since the input voltage and current are directly related to the transformer's maximum load capacity, it is more appropriate to express the rating in kVA, which represents the product of voltage and current.

Step-by-step solution

Maximum load per home

Given, each home has a fuse that limits the incoming current to 60A rms at 220V rms. The maximum load each home can safely consume is given by the formula: Load (Per Home) = Voltage × Current Calculate the maximum load per home. Load (Per Home) = 220V × 60A = 13,200W

Total load on the transformer

There are four homes connected to the transformer. To find the total load on the transformer, add the loads of each home. Total Load = Load (Per Home) × Number of Homes Total Load = 13,200W × 4 = 52,800W = 52.8kW Now, convert this load to kVA. We know that: Power (kVA) = Power (kW) × Power Factor Assuming a power factor of 1 (which is the maximum possible value). Total Load (kVA) ≈ 52.8kVA (Approximated as the power factor is not provided).

Checking the adequacy of the transformer rating

The rating of the transformer is given as 35 kV⋅A. Compare the total load on the transformer to its rating. Total Load (kVA) = 52.8kVA Transformer Rating = 35kVA Since the total load (52.8kVA) exceeds the transformer rating (35kVA), the transformer is NOT adequate to handle the load.

Explain why the transformer rating is given in kV⋅A rather than kW.

Transformer ratings are given in kVA because transformers deal with voltages and currents, not power directly. In an AC circuit, the power is given as: Power (kW) = Voltage (V) × Current (A) × Power Factor The power factor is a measure of how efficiently the input power is converted into useful output power. The power factor ranges between 0 and 1, with 1 representing the most efficient conversion. Since the input voltage and current are directly related to the transformer's maximum load capacity, it is more appropriate to express the rating in kVA, which represents the product of voltage and current.