Question

An ac generator generates an emf which is given by e = 311 sin (240 πt) V. Calculate:

1. frequency of the emf.
2. r.m.s. value of the emf.

Answer 1

(1) Given that

e = 311 sin (240 πt) V   ...(i)

∵ e = e₀ sin (ωt) V     ...(ii)

From equations (i) and (ii)

e₀ = 311 and ωt = 240 πt

∴ ω = 240 π

f = `omega/(2pi)`

`= (240  pi)/(2pi)`

= 120 cycle/s

e₀ = Peak emf of the generator = 33

∵ Peak emf = rms · emf × `sqrt2`

∴ rms = `1/sqrt2` peak emf

= 0.707 × 311 = 219.87 volts

∴ rms = 219.87 volts

(2) Given the number of turns in the primary winding is N_P = 60 turns.

The number of turns in secondary winding is N_S = 3000 turns.