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

V_o

$fraction numerator straight V subscript straight o over denominator square root of 2 end fraction$

V_o/2

$fraction numerator straight V subscript straight o over denominator square root of 3 end fraction$

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Solution

fraction numerator straight V subscript straight o over denominator square root of 2 end fraction

straight V subscript rms space equals space open square brackets 1 over straight T integral subscript 0 superscript straight T divided by 2 end superscript straight V subscript 0 superscript 2 dt close square brackets to the power of 1 divided by 2 end exponent equals space open square brackets fraction numerator straight V subscript 0 superscript 2 over denominator straight T end fraction left square bracket straight t right square bracket subscript 0 superscript straight T divided by 2 end superscript close square brackets to the power of 1 divided by 2 end exponent equals space open square brackets fraction numerator straight V subscript 0 superscript 2 over denominator 2 end fraction open parentheses straight T over 2 close parentheses close square brackets to the power of 1 divided by 2 end exponent straight V subscript rms space equals space open square brackets fraction numerator straight v subscript 0 superscript 2 over denominator 2 end fraction close square brackets to the power of 1 divided by 2 end exponent straight v subscript rms space equals space fraction numerator straight V subscript 0 over denominator square root of 2 end fraction

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