---
title: "Alternator open-circuit emf at 40 Hz"
subject: "Electrical Machine"
chapter: 6
key: "semester_4/electrical_machine:alternator-oc-360v-field-current"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/alternator-oc-360v-field-current
site: BCT Engineering
---

# Alternator open-circuit emf at 40 Hz

Electrical Machine · Chapter 6: Three Phase Synchronous Machines

- Asked in: 2075 Baisakh, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/alternator-oc-360v-field-current
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-6

## Question

An alternator on open circuit generates 360 V at 60 Hz, when the field current is 3.6 A. Neglecting saturation, determine the open circuit emf. When the frequency is 40 Hz and the field current is 2.4 A.

## Short answer

Emf is proportional to frequency and field current: E2 = E1 × (f2/f1) × (If2/If1) = 360 × (40/60) × (2.4/3.6) = 160 V. The open-circuit emf is 160 V.

## Answer

**Given:** open-circuit emf E₁ = 360 V at f₁ = 60 Hz with field current I_f1 = 3.6 A. Find E₂ at f₂ = 40 Hz and I_f2 = 2.4 A. Saturation is neglected.

The induced emf per phase is E = 4.44 f Φ T_ph K_w. T_ph and K_w are fixed by the winding. Without saturation, flux per pole Φ is proportional to the field current. So

**E ∝ f · I_f**

```text
 E2 / E1 = (f2 / f1) × (If2 / If1)
         = (40 / 60) × (2.4 / 3.6)
         = 0.6667 × 0.6667 = 0.4444

 E2 = 0.4444 × 360 = 160 V
```
The frequency changes because the speed changes (f = PN/120), so the speed is 40/60 = 2/3 of the original and the flux is 2/3 of the original.

**Answer: open-circuit emf = 160 V (on the same basis, line or phase, as the given 360 V).**

## Check yourself

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

1. Without saturation, E is proportional to what?
   A. f x If
   B. f / If
   C. If only
   D. f^2
   Answer: A. E = 4.44 f Phi T Kw, and Phi is proportional to If. (Key point: Dependence of emf)

2. Why does flux scale by 2/3 along with frequency?
   A. Field current is 2/3, so flux is 2/3
   B. Speed is 2/3 so flux is 2/3
   C. Turns change
   D. Winding factor changes
   Answer: A. Phi follows If = 2.4/3.6 = 2/3; frequency changes because speed is 2/3. (Key point: Frequency ratio)

3. What is E2?
   A. 240 V
   B. 160 V
   C. 360 V
   D. 100 V
   Answer: B. E2 = 360 x (2/3) x (2/3) = 160 V. (Key point: Result)

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