AIIMS2018Physics-Electromagnetic Induction

AIIMS 2018 Physics RMS Voltage MCQ Question

Type: MCQ-numerical-Medium-Class 12

The voltage-time (VtV-t) graph for a triangular wave having peak value V0V_0 is as shown in figure. The rms value of VV in the time interval from t=0t = 0 to T/4T/4 is V0x\frac{V_0}{\sqrt{x}}, then find the value of xx.

Question diagram
A

5

B

4

C

7

D

3

Correct Answer

Option D

Detailed Explanation

The equation V=4V0TtV = \frac{4V_0}{T} t indicates that the voltage VV is directly proportional to time tt and the maximum voltage V0V_0. At t=T4t = \frac{T}{4}, substituting this value into the equation gives V=4V0TT4=V0V = \frac{4V_0}{T} \cdot \frac{T}{4} = V_0, confirming that the voltage reaches its maximum value V0V_0 at this point.

Options (A) V03\frac{V_0}{\sqrt{3}}, (B) V02\frac{V_0}{2}, and (C) V02\frac{V_0}{\sqrt{2}} suggest values less than V0V_0, which do not correspond to the maximum voltage reached in the given equation at t=T4t = \frac{T}{4}.

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