The rms value of emf given by E = (8 sin ω t + 6 cos ω t) volt is

Question

The rms value of emf given by E = (8 sin ω t + 6 cos ω t) volt is (A) 5 √2 V  (B) 7 √2 V  (C) 10 V  (D) 10 √2 V

Tardigrade Admin · Accepted Answer

E=(8 sin ω t+6 cos ω t) =(A cos θ sin ω t-A sin θ cos ω t) where, A cos θ= 8 and A sin θ=6 A2( cos 2 θ+ sin 2 θ)=82+62=100 A =10 rms value, E rms =(A/√2)=(10/√2) =(5 × 2/√2)=5 √2

Q. The rms value of emf given by $E = (8 sin ω t + 6 cos ω t)$ volt is

$52 V$

$72 V$

$10 V$

$102 V$

$E = (8 sin ω t + 6 cos ω t)$
$= (A cos θ sin ω t - A sin θ cos ω t)$
where, $A cos θ = 8$ and $A sin θ = 6$
$A^{2} (cos^{2} θ + sin^{2} θ) = 8^{2} + 6^{2} = 100$
$A = 10$
rms value, $E_{r m s} = \frac{A}{2} = \frac{10}{2}$
$= \frac{5 \times 2}{2} = 52$

Q. The rms value of emf given by E=(8sinωt+6cosωt) volt is

52​V

72​V

10V

102​V