Penny-Arcade EEs: this is an incredibly simple problem, and yet I am stuck on it.

A single-phase two-winding transformer has 1000 turns on the primary and 500 turns on the secondary. The primary winding is connected to a 220V supply and the secondary winding is connected to a 5 kVA load. The transformer can be considered ideal. Determine (a) the load voltage, (b) the load impedance and (c) the load impedance referred to the primary.

Right. So, for part (a), V1/V2 = N1/N2, and V2=110V.

Part (b) is where I'm stuck. How can I find the impedance given the apparent power? S = 5 kVA = V2rms I2rms, so I2rms is 64.284.

Close, but not quite. I'm not sure why you've written down the peak current, especially since you've written I2rms. 5kVA/110V = 45.46V ...?

But how can I find the impedance without knowing the angle between I2 and V2?

Presumably, what they want in this case is just the magnitude of the impedance. Since you know the magnitude of V2 and I2, you can then determine the magnitude of Z2.

It wasn't specified, so I was assuming the given 220V was peak voltage, making V2=110V a peak value with an RMS of 77.78V, so 5000/77.78 = 64.284.

No no, any and all quoted voltages, currents and powers are always in RMS unless explicitly stated or expected to be otherwise. If you ever stand back and ask, "Hey, is that RMS or something else?", then chances are good that it's RMS.

Peak is quote often a terrible measure to use since it implicitly assumes that the reader has knowledge of the shape of the waveform. For example, in your question above, you assumed that the input was perfectly sinusoidal. However, this is not always the case - even for mains voltages (it wouldn't be unexpected to see a bit of third/five harmonic in the mains chopping off the top of the sine wave so that the peak ends up lower than expected. A consequence of the standard transformer-rectifier-dc capacitor design decision).

## Posts

Close, but not quite. I'm not sure why you've written down the peak current, especially since you've written I2rms. 5kVA/110V = 45.46V ...?

Presumably, what they want in this case is just the magnitude of the impedance. Since you know the magnitude of V2 and I2, you can then determine the magnitude of Z2.

ecco the dolphinonTaximesonNo no, any and all quoted voltages, currents and powers are

alwaysin RMS unless explicitly stated or expected to be otherwise. If you ever stand back and ask, "Hey, is that RMS or something else?", then chances are good that it's RMS.Peak is quote often a terrible measure to use since it implicitly assumes that the reader has knowledge of the shape of the waveform. For example, in your question above, you assumed that the input was perfectly sinusoidal. However, this is not always the case - even for mains voltages (it wouldn't be unexpected to see a bit of third/five harmonic in the mains chopping off the top of the sine wave so that the peak ends up lower than expected. A consequence of the standard transformer-rectifier-dc capacitor design decision).

ecco the dolphinon