Variation of voltage with time is shown in figure.
The rms voltage is found to be , $N \sqrt{\frac{2}{3}} V$ . Find N.

Question

Variation of voltage with time is shown in figure.The rms voltage is found to be ,$$N23V$$. Find N.

Infinity Learn · Accepted Answer

In such cases it is difficult to develop a single equation.

Hence, it is usual to consider two equations, one applicable from 0 to 1 ms and another from 1 to 2 ms.
For t lying between 0 and 1 ms, V₁ = 4. For t lying between 1 and 2 ms, V₂= -4t+4.

(a) $V_{r m s} = \sqrt{\frac{1}{2} (\int_{0}^{1} V_{1}^{2} d t + \int_{1}^{2} V_{2}^{2} d t)}$

$V_{r m s}^{2} = \frac{1}{2} [\int_{0}^{1} 4^{2} d t + \int_{1}^{2} {(- 4 t + 4)}^{2} d t]$

$= \frac{1}{2} [{|16 t|}_{0}^{1} + {|\frac{16 t^{3}}{3}|}_{1}^{2} + {| 16 t |}_{1}^{2} - {|\frac{32 t^{2}}{2}|}_{1}^{2}] = \frac{32}{3}$

$V_{r m s} = \sqrt{\frac{32}{3}} = 4 \sqrt{\frac{2}{3}} V . H e n c e N = 4$

Alternating Current and voltage

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Variation of voltage with time is shown in figure.
The rms voltage is found to be , $N \sqrt{\frac{2}{3}} V$ . Find N.

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Alternating Current and voltage

Unlock the full solution & master the concept.

Variation of voltage with time is shown in figure.The rms voltage is found to be ,N23V. Find N.

Ready to Test Your Skills?

free study material

Variation of voltage with time is shown in figure.
The rms voltage is found to be , $N \sqrt{\frac{2}{3}} V$ . Find N.