MCQ
The $r.m.s.$ value of potential difference $V$ shown in the figure is
- A$\frac{{V_0}}{{\sqrt 3 }}$
- B$V_0$
- ✓$\frac{{V_0}}{{\sqrt 2 }}$
- D$\frac{{V_0}}{2}$
✓
Answer
Correct option: C.
$\frac{{V_0}}{{\sqrt 2 }}$
c
$V=V_{0}$ for $0 \leq t \leq \frac{T}{2}$
$V=V_{0}$ for $0 \leq t \leq \frac{T}{2}$
$V=0$ for $\frac{T}{2} \leq t \leq T$
${V_{rms}} = \left[ {\frac{{\int\limits_0^T {{V^2}\,dt} }}{{\int\limits_0^T {dt} }}} \right] = {\left[ {\frac{{\int\limits_0^{T/2} {V_0^2\,dt} + \int\limits_{T/2}^T {(0)\,dt} }}{{\int\limits_0^T {dt} }}} \right]^{1/2}}$
$ = {\left[ {\frac{{V_0^2}}{T}[t]_0^{T/2}} \right]^{1/2}}$
$ = {\left[ {\frac{{V_0^2}}{T}\left( {\frac{T}{2}} \right)} \right]^{1/2}}$
$ = {\left[ {\frac{{V_0^2}}{2}} \right]^{1/2}}$
${V_{rms}} = \frac{{{V_0}}}{{\sqrt 2 }}$
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