Question

The RMS value of a rectangular wave of period T, having a value of +V for a duration T1 (< T) and −V for the duration T − T1 = T2, equals _____________

(a) V

(b) \(\frac{V}{\sqrt{2}}\)

(c) \(\frac{T_1-T_2}{T}\) V

(d) \(\frac{T_1}{T_2}\) V

The question was posed to me during an internship interview.

Enquiry is from Miscellaneous Examples on Fourier Series topic in chapter Fourier Series of Signals and Systems

Answer 1

The correct option is (a) V

The explanation is: Period = T = T1 + T2

RMS value = \(\sqrt{\frac{1}{T} ∫_0^T x^2 (t)dt}\)

= \(\sqrt{\frac{1}{T}[V^2.(T_1 – 0) + V^2 (T – T_1)]}\)

= \(\sqrt{V^2}\)

= V.