Electro Magnetic Induction And Alternating Currents Question 143

Question: Match the following Currents r.m.s. values (1) $ x_{0}\sin \omega ,t $ (i) x0 (2) $ x_{0}\sin \omega ,t\cos \omega ,t $ (ii) $ \frac{x_{0}}{\sqrt{2}} $ (3) $ x_{0}\sin \omega ,t+x_{0}\cos \omega ,t $ (iii) $ \frac{x_{0}}{(2\sqrt{2})} $

Options:

A) 1. (i), 2. (ii), 3. (iii)

B) 1. (ii), 2. (iii), 3. (i)

C) 1. (i), 2. (iii), 3. (ii)

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  1. rms value = $ \frac{x_{0}}{\sqrt{2}} $

  2. $ x_{0}\sin \omega t\cos \omega t=\frac{x_{0}}{2}\sin 2\omega t\Rightarrow rms\ value =\frac{x_{0}}{2\sqrt{2}} $

  3. $ x_{0}\sin \omega t+x_{0}\cos \omega t\Rightarrow rms\ value = \sqrt{{{( \frac{x_{0}}{\sqrt{2}} )}^{2}}+{{( \frac{x_{0}}{\sqrt{2}} )}^{2}}} $ $ =\sqrt{x_{0}^{2}}=x_{0} $



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