A waveform is of the form of a trapezium, which increases linearly with the linear slope till θ = \(\frac{π}{3}\), constant till θ = \(\frac{π}{2}\) and again linearly decreases to 0 till θ = π. The average value of this waveform is ______________(a) 2 V(b) 0 V(c) 4 V(d) 3 VI have been asked this question in exam.The question is from Advanced Problems Involving Complex Circuit Diagram in portion Network Theory and Complex Circuit Diagram of Network Theory

A waveform is of the form of a trapezium, which increases linearly wit

1.	A waveform is of the form of a trapezium, which increases linearly with the linear slope till θ = \(\frac{π}{3}\), constant till θ = \(\frac{π}{2}\) and again linearly decreases to 0 till θ = π. The average value of this waveform is ______________(a) 2 V(b) 0 V(c) 4 V(d) 3 VI have been asked this question in exam.The question is from Advanced Problems Involving Complex Circuit Diagram in portion Network Theory and Complex Circuit Diagram of Network Theory
Answer» The CORRECT OPTION is (d) 3 V To explain: The average value of the waveform = \(\frac{2 X AREA \,of \,1st \,triangle\, + \,Area \,of\, 2nd \,triangle}{π}\) = \(\frac{2 X \frac{π}{3} X \frac{1}{2} X 6 + 6(\frac{π}{2} – \frac{π}{3})}{π}\) = \(\frac{2π + π}{π}\) = 3 VOLT.

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