The rms value of potential difference V0 shown in figure is

Question

The rms value of potential difference V0 shown in figure is (A)  V0  (B)  (V0/√2)  (C)  (V0/2 )  (D)  (V0/√3)

Tardigrade Admin · Accepted Answer

Given, Vrms2 = (1/T) ∫ limits0T V2 dt = (1/T) ∫ limits0(T/2)V20 dt + (1/T) ∫ limits(T/2)T 0 dt = (V02 /T) × (T/2) = (V02/2) ∴ According to the given figure, ∴ Vrms = (V02/√2)

Q. The $r m s$ value of potential difference $V_{0}$ shown in figure is

$V_{0}$

$\frac{V _{0}}{2}$

$\frac{V _{0}}{2}$

$\frac{V _{0}}{3}$

Given, $V_{r m s}^{2} = \frac{1}{T} 0 \int T V^{2} d t$
$= \frac{1}{T} 0 \int \frac{T}{2} V_{0}^{2} d t + \frac{1}{T} \frac{T}{2} \int T 0 d t$
$= \frac{V _{0}^{2}}{T} \times \frac{T}{2} = \frac{V _{0}^{2}}{2}$
$∴$ According to the given figure,
$∴ V_{r m s} = \frac{V _{0}^{2}}{2}$

Q. The rms value of potential difference V0​ shown in figure is

V0​

2​V0​​

2V0​​

3​V0​​

Given, Vrms2​=T1​0∫T​V2dt =T1​0∫2T​​V02​dt+T1​2T​∫T​0dt =TV02​​×2T​=2V02​​ ∴ According to the given figure, ∴Vrms​=2​V02​​

Q. The $r m s$ value of potential difference $V_{0}$ shown in figure is

$V_{0}$

$\frac{V _{0}}{2}$

$\frac{V _{0}}{2}$

$\frac{V _{0}}{3}$

Given, $V_{r m s}^{2} = \frac{1}{T} 0 \int T V^{2} d t$
$= \frac{1}{T} 0 \int \frac{T}{2} V_{0}^{2} d t + \frac{1}{T} \frac{T}{2} \int T 0 d t$
$= \frac{V _{0}^{2}}{T} \times \frac{T}{2} = \frac{V _{0}^{2}}{2}$
$∴$ According to the given figure,
$∴ V_{r m s} = \frac{V _{0}^{2}}{2}$