Question

The rms value of emf given by e=8sin(wt)+6cos(wt)is

Answer 1

Answer:

emf rms = 5 √2 volts.

Step-by-step explanation:

Given sinusoidal  wave form :

  e = 8 Sin ωt + 6 Cos ωt

e = voltage.  ω = angular frequency. t = time.

   Let Sin Ф = 6/√(8²+6²) = 3/5.   Cos Ф = 8/√(8²+6²) = 4/5

  So   e = 10 * (Cos Ф Sin ωt +Sin Ф Cos ωt)

  e = 10 Sin (ωt + Ф)

  Time period = T = 2π/ω  

$e_{rms}^2=\frac{100}{T} \int \limits_{0}^{T} | e(t) |^2 dt\\\\=\frac{100}{T} \int \limits_{0}^{T} Sin^2(\omega t+\phi) \, dt\\\\=\frac{100}{T} * \frac{1}{2} \int \limits_{0}^{T} (1-Cos(2\omega t + 2\phi)) \, dt\\\\=\frac{100}{2T} * (t-Sin (2\omega t +2 \phi))_0^T \\\\ = \frac{100}{2T}*(T) =50 \\\\e_{rms}=\sqrt{50}=5 \sqrt{2} \, volts$

emf = 5√2 volts.

Answer 2

Answer:

Refers to the attachment