---
title: "Reason: losses depend on frequency"
subject: "Electrical Machine"
chapter: 1
key: "semester_4/electrical_machine:eddy-hysteresis-frequency-reason"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/eddy-hysteresis-frequency-reason
site: BCT Engineering
---

# Reason: losses depend on frequency

Electrical Machine · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2071 Bhadra, 4 marks
- Video: [Eddy current & Eddy Current loss | Electrical Engineering](https://www.youtube.com/watch?v=XPk38Tz_UC0) — Gaurav J - TheElectricalGuy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/eddy-hysteresis-frequency-reason
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-1

## Question

Give reason: Hysteresis and eddy current losses depend on the frequency of supply system.

## Short answer

Hysteresis loss per cycle is constant, so total loss P_h ∝ f. Eddy current loss arises from induced emf proportional to f, and power loss I²R ∝ f², so P_e ∝ f². Hence both losses increase with supply frequency.

## Answer

Both losses are directly tied to how often the flux reverses, so they increase with the supply frequency.

#### Hysteresis loss
- In every cycle the core material is taken round one complete B–H loop. The energy lost per cycle per unit volume equals the area of the loop (a fixed amount for given B_max).
- If the supply has *f* cycles per second, the loop is traversed *f* times a second. So the loss per second is (area × volume × f).
- **Pₕ = ηₕ B_max^1.6 f V**, so Pₕ ∝ f.

#### Eddy current loss
- The emf induced in the core is proportional to the rate of change of flux, e ∝ dφ/dt. For a sinusoidal flux, E ∝ f B_max.
- The eddy current is proportional to this emf: I ∝ f B_max.
- The power loss is I²R, so it varies as the square of the emf.
- **Pₑ = kₑ B_max² f² t² V**, so Pₑ ∝ f².

Example: if the frequency of the same transformer is doubled at constant B_max, hysteresis loss doubles and eddy current loss becomes four times. This is why 50 Hz transformers are not suitable for operation at high frequency without redesign, while 400 Hz equipment uses thinner laminations.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is hysteresis loss proportional to f?
   A. The loop area grows with f squared
   B. Flux grows with f
   C. The loop is traversed f times per second, each costing a fixed energy
   D. Resistance rises with f
   Answer: C. Energy per cycle (loop area x volume) is fixed for a given Bmax, so power is that times f. (Key point: Hysteresis vs frequency)

2. Why is eddy current loss proportional to f^2?
   A. Emf is proportional to f, current is proportional to emf, and loss is I^2R
   B. Resistance is proportional to f^2
   C. Loss is proportional to emf only
   D. Flux is proportional to f^2
   Answer: A. E is proportional to f Bmax, so I is proportional to f, and I^2 R gives f^2. (Key point: Eddy vs frequency)

3. At constant Bmax, if frequency is doubled, what happens?
   A. Hysteresis becomes four times, eddy loss doubles
   B. Hysteresis doubles, eddy current loss becomes four times
   C. Both become four times
   D. Both losses double
   Answer: B. Ph is proportional to f (x2) and Pe to f^2 (x4). (Key point: Doubling frequency)

## Related in Electrical Machine

- [Hysteresis and eddy losses depend on frequency](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ahysteresis-eddy-frequency-reason) — Electrical Machines, chapter 1
- [Hysteresis and eddy current losses; loop area](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Ahysteresis-eddy-loss-area) — Electrical Machine, chapter 1
- [Hysteresis and eddy current losses, reduction](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ahysteresis-eddy-losses-reduce) — Electrical Machines, chapter 1

## Related in other subjects

- [Hysteresis loss and eddy current loss](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Ahysteresis-eddy-loss) — Electric Machine Design, chapter 1