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RMS Value of Current in Sinusoidal AC

The rms value...

Question

The rms value of potential difference V shown in figure is :

V_{o}

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V_{o} / 2

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V_{o} / \sqrt{2}

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V_{o} / \sqrt{3}

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Solution

The correct option is C $V_{o} / \sqrt{2}$
Voltage is given as $V = V_{o}$ for $0 \geq t \leq T / 2$

$= 0$ for $T / 2 \geq t \leq T$

Rms voltage $V_{r m s} = \sqrt{\frac{\int_{o}^{T} V^{2} d t}{T}}$

Or $V_{r m s} = \sqrt{\frac{\int_{o}^{T / 2} V_{o}^{2} d t}{T} + \frac{\int_{T / 2}^{T} 0 d t}{T}}$

Or $V_{r m s} = \sqrt{\frac{\int_{o}^{T / 2} V_{o}^{2} d t}{T}}$

Or $V_{r m s} = \sqrt{\frac{V_{o}^{2} \times T / 2}{T}}$

$⟹ V_{r m s} = V_{o} / \sqrt{2}$

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