Question

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 V

I 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 1

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.