The rms value of the potential difference v s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The root mean square (rms) value of a periodic function $v(t)$ is defined as $V_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} v^2(t) dt}$.From the given

Vedclass · Accepted Answer

$\frac{v_{0}}{\sqrt{2}}$

Vedclass · Answer

(D) The root mean square (rms) value of a periodic function $v(t)$ is defined as $V_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} v^2(t) dt}$.From the given figure, the potential difference $v(t)$ is $V_0$ for the interval $0 \le t Thus, $V_{rms}^2 = \frac{1}{T} \left[ \int_{0}^{T/2} V_0^2 dt + \int_{T/2}^{T} 0^2 dt \right]$.$V_{rms}^2 = \frac{1}{T} \left[ V_0^2 \cdot \frac{T}{2} + 0 \right] = \frac{V_0^2}{2}$.Taking the square root on both sides, we get $V_{rms} = \frac{V_0}{\sqrt{2}}$.

Currents	$r.m.s.$ values
$(A) \ x_0 \sin \omega t$	$(i) \ x_0$
$(B) \ x_0 \sin \omega t \cos \omega t$	$(ii) \ \frac{x_0}{\sqrt{2}}$
$(C) \ x_0 \sin \omega t + x_0 \cos \omega t$	$(iii) \ \frac{x_0}{2\sqrt{2}}$

The rms value of the potential difference $v$ shown in the figure is

Similar Questions

The rms value of the emf given by $E = (8 \sin \omega t + 6 \cos \omega t) \text{ V}$ is:

Match the following:

Currents $r.m.s.$ values

$(A) \ x_0 \sin \omega t$ $(i) \ x_0$

$(B) \ x_0 \sin \omega t \cos \omega t$ $(ii) \ \frac{x_0}{\sqrt{2}}$

$(C) \ x_0 \sin \omega t + x_0 \cos \omega t$ $(iii) \ \frac{x_0}{2\sqrt{2}}$

The a.c. source of e.m.f. with instantaneous value $e$ is given by $e = 200 \sin(50t) \text{ V}$. The r.m.s. value of current in a circuit of resistance $50 \ \Omega$ is: (in $\text{ A}$)

The variation of $EMF$ with time for four types of generators is shown in the figures. Which amongst them can be called $AC$?

The $ rms $ value of current in a $ 50 \,Hz $ $ AC $ circuit is $ 6 \,A $. The average value of $ AC $ current over a complete cycle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module