Question

The rms value of emf given by $E = (8 \, \sin \, \omega t + 6 \, \cos \omega t)$ volt is

• A. $5 \sqrt{2} V $
• B. $7 \sqrt{2} V $
• C. $10 \, V $
• D. $10 \sqrt{2} V $

Answer 1

Answer: (A)

$E=(8 \sin \omega t+6 \cos \omega t)$
$=(A \cos \theta \sin \omega t-A \sin \theta \cos \omega t)$
where, $A \cos \theta= 8$ and $A \sin \theta=6$
$A^{2}\left(\cos ^{2} \theta+\sin ^{2} \theta\right)=8^{2}+6^{2}=100$
$A =10$
rms value, $E_{ rms } =\frac{A}{\sqrt{2}}=\frac{10}{\sqrt{2}}$
$=\frac{5 \times 2}{\sqrt{2}}=5 \sqrt{2}$