Question

The rms value of a half-wave rectified symmetrical square wave current of 2a is: (a) 2a (b) 1a (c) 1 2a (d) 3a

Answer 1

Answer:

Answer is  square root of 2 Amp.  √2 amp. But it is not in the given options.  

Step-by-step explanation:

 See the enclosed diagram showing the waveform and the rectified waveform.

We need the formula for the rms value. We use integration.

 $I_{rms}^2=\frac{1}{T} \int \limits_{-\frac{T}{2}}^{\frac{T}{2}} | I (t) |^2 dt\\\\=\frac{1}{T} \int \limits_{-\frac{T}{2}}^{0} | 0 |^2 dt+\frac{1}{T} \int \limits_{0}^{\frac{T}{2}} | 2 |^2 dt\\\\=\frac{1}{T} * 4 * \frac{T}{2} =2\\\\I_{rms}=\sqrt{2} \ Amp$

So it is square root of 2 amp.