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Question

The rms value of potential difference V shown in figure is :
595823.jpg


A
Vo
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B
Vo/2
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C
Vo/2
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D
Vo/3
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Solution

The correct option is C $$V_o/\sqrt2$$
Voltage is given as    $$V = V_o$$   for   $$0\geq t\leq T/2 $$

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

Rms voltage    $$V_{rms} = \sqrt{\dfrac{\int^T_o V^2 dt}{T}}$$

Or   $$V_{rms} = \sqrt{\dfrac{\int^{T/2}_o V_o^2 dt}{T}+\dfrac{\int_{T/2}^T 0 \ dt}{T}}$$

Or   $$V_{rms} = \sqrt{\dfrac{\int^{T/2}_o V_o^2 dt}{T}}$$

Or   $$V_{rms} = \sqrt{\dfrac{V_o^2 \times T/2}{T}}$$

$$\implies \ V_{rms} = V_o/\sqrt{2}$$

Physics
NCERT
Standard XII

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