If the rms value of the voltage of the waveform shown below is (p)/(q) V , then what is the value of (p + q) ? ( p and q are the smallest positive integers.)

Correct answer: D. 7 V _ rms ^ 2 = 1 T ∫ _ 0 ^ T V ^ 2 dt = 2 T ∫ _ 0 ^ T 2 V ^ 2 dt T = 2 sec, V = 2t 0 ≤ t ≤ 1 V _ rms ^ 2 = 2 T ∫ _ 0 ^ 1 4 t ^ 2 dt = ∫ _ 0 ^ 1 4 t ^ 2 dt = 4 t ^ 3 3 ] _ 0 ^ 1 = (4)/(3) V _ rms = (4)/(3) V

NEET

Exam: NEET
Subject: Physics
Chapter: Alternating Current

NEET · Physics · Alternating Current

If the rms value of the voltage of the waveform shown below is...

If the rms value of the voltage of the waveform shown below is

\sqrt{\dfrac{p}{q}}V

, then what is the value of \left(p + q\right)

? (

p and q$ are the smallest positive integers.)

Options

Correct answer

D. 7

Step-by-step solution

{\text{V}}_{\text{rms}}^{2} = \dfrac{1}{\text{T}} \mathop{∫}_{0}^{\text{T}} {\text{V}}^{2} \text{dt} = \dfrac{2}{\text{T}} \mathop{∫}_{0}^{\dfrac{\text{T}}{2}} {\text{V}}^{2} \text{dt}

T = 2 sec,

V = 2t

0 \le \text{t} \le 1

{\text{V}}_{\text{rms}}^{2} = \dfrac{2}{\text{T}} \mathop{∫}_{0}^{1} 4 {\text{t}}^{2} \text{dt}

= \mathop{∫}_{0}^{1} 4 {\text{t}}^{2} \text{dt}

= 4 \dfrac{{\text{t}}^{3}}{3} {]}_{0}^{1} = \dfrac{4}{3}

{\text{V}}_{\text{rms}} = \sqrt{\dfrac{4}{3}}\text{V}

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