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Sinusoidal AC

The r.m.s. va...

Question

The r.m.s. value of potential due to superposition of given two alternating potentials $E_{1} = E_{0}$ sin $ω t$ and $E_{2} = E_{0}$ cos $ω t$ will be :

E_{0}

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2 E_{0}

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E_{0} \sqrt{2}

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Zero

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Solution

The correct option is C $E_{0}$
Superposition of $E_{1}$ and $E_{2} \Rightarrow E = E_{0} s i n ω t + E_{0} c o s ω t = \sqrt{2} E_{0} C o s (45^{\circ} - ω t)$

R.M.S. value of $E$ is given as
$E_{r m s}^{2} = \frac{1}{T} \int_{0}^{T} E^{2} d t$ , where $T =$ $\frac{2 π}{ω}$

On integrating, $E_{r m s} = \sqrt{2} \frac{E_{0}}{\sqrt{2}} = E_{0}$ .

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