Topic: Network Theory
The rms value of the periodic waveform as shown in Figure is
- A. $\sqrt{3/2}A$
- B. $\sqrt{2/3}A$
- C. $\sqrt{1/3}A$
- D. $\sqrt{2}A$
Answer: B. $\sqrt{2/3}A$
Explanation: $V_{rms}=\sqrt{\frac{1}{T}\int_{0}^{T}V^{2}dt}$. $V_{rms}=\sqrt{\frac{1}{T}\left[\int_{0}^{T/2}\left(\frac{2A}{T}t\right)^{2}dt+\int_{T/2}^{T}(-A)^{2}dt\right]} = \sqrt{\frac{1}{T}\left[\frac{4A^{2}}{T^{2}}\left(\frac{t^{3}}{3}\right)_{0}^{T/2}+A^{2}[t]_{T/2}^{T}\right]} = \sqrt{\frac{4A^{2}}{3T^{3}}\cdot\frac{T^{3}}{8}+\frac{A^{2}}{T}\cdot\frac{T}{2}} = A\sqrt{\frac{1}{6}+\frac{1}{2}}=A\sqrt{\frac{2}{3}}$.