First slide

Alternating current and voltage

Question

The rms value of potential difference V shown in the fig. 10.56 is :

Moderate

A

$\frac{V_{0}}{\sqrt{3}}$
B

V₀
C

$\frac{V_{0}}{\sqrt{2}}$
D

$\frac{V_{0}}{2}$

Solution

$V_{rms} = \sqrt{\frac{\int_{0}^{T} V^{2} dt}{\int_{0}^{T} dt}} = \sqrt{\frac{\int_{0}^{T / 2} {V_{0}}^{2} dt + \int_{T / 2}^{T} 0^{2} dt}{T}} = \sqrt{\frac{{V_{0}}^{2} (\frac{T}{2})}{T}} = \frac{V_{0}}{\sqrt{2}}$

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