Question

In the figure given below, what is the RMS value of the periodic waveform?

(a) 2\(\sqrt{6}\) A

(b) 6\(\sqrt{2}\) A

(c) \(\sqrt{\frac{4}{3}}\) A

(d) 1.5 A

This question was addressed to me in a job interview.

My query is from Dot Convention in Magnetically Coupled Circuits topic in section Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

The correct option is (a) 2\(\sqrt{6}\) A

The explanation is: The rms value for any waveform is = \(\sqrt{\frac{1}{T} \int_0^T f^2 (t)dt)}\)

= \([\frac{1}{T}(\int_0^{\frac{T}{2}}(mt)^2 dt + \int_{\frac{T}{2}}^T 6^2 dt]^{1/2}\)

= \([\frac{1}{T}(\frac{144}{T^2}  × \frac{T^3}{3×8} + 36 × \frac{T}{2})]^{\frac{1}{2}}\)

= \([6+18]^{\frac{1}{2}} = \sqrt{24} = 2\sqrt{6}\) A.