Question

An alternating emf is given by e = 220 sin 314.2 t (in volt). Find its 

(i) peak value 

(ii) rms value 

(iii) average value over half cycle 

(iv) frequency 

(iv) period 

(vi) value at T/4.

Answer 1

Data: e = 220 sin314.2t (in volt), t = \(\cfrac T4\)

(i) Comparing the given equation with e = e₀ sin

ωt, we get, peak value, e₀ = 220V.

(ii) e_rms = = e₀/√ 2 = 155.6 V

(iii) e_av (over half cycle) = \(\cfrac2{\pi}\)e₀ = \(\cfrac{2(220)}{3.142}\) = 140 V

(iv) ω = 2πf= 314.2 ∴ The frequency,

f = \(\cfrac{ω}{2\pi}\) = \(\cfrac{314.2}{2(3.142)}\) = 50 Hz

(v) The period, T = \(\cfrac 1f\) = \(\cfrac 1{50}\) = 0.02 same

(vi) e = 220 sin \(\left(\cfrac{2\pi}T.{\cfrac T4}\right)\) = 220 sin \(\cfrac{\pi}2\) = 220 v