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Q.
The r.m.s. value of potential differenced $V$ shown in the figure is
AIPMTAIPMT 2011Alternating Current
Solution:
Voltage is given as $V = V _{0}$
for $0 \geq t \leq T / 2$
$=0$ for $T / 2 \geq t \leq T$
Rms voltage $ V_{r m s}=\sqrt{\frac{\int\limits_{0}^{T} V^{2} d t}{T}}$
Or $V _{ rms }=\sqrt{\frac{\int\limits_{0}^{ T / 2} V _{0}^{2} dt }{ T }+\frac{\int\limits_{ T / 2}^{ T } 0 dt }{ T }}$
Or $V_{ rms }=\sqrt{\frac{\int\limits_{0}^{ T / 2} V _{0}^{2} dt }{ T }}$
Or $V _{ rms }=\sqrt{\frac{ V _{0}^{2} \times T / 2}{ T }}$
$\Rightarrow V _{ rms }= V _{ o } / \sqrt{2}$
