Electro Magnetic Induction And Alternating Currents Question 142
Question: In a certain circuit current changes with time according to $ i=2\sqrt{t}. $ r.m.s. value of current between $ t=2 $ to $ t=4s $ will be
Options:
A) $ 3A $
B) $ 3\sqrt{3}A $
C) $ 2\sqrt{3}A $
D) $ (2-\sqrt{2})A $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \overline{i^{2}}=\frac{\int_{{}}^{{}}{i^{2}dt}}{\int_{{}}^{{}}{dt}}=\frac{\int_{2}^{4}{(4t)}dt}{\int_{2}^{4}{dt}}=\frac{4\int_{2}^{4}{t\ dt}}{2} $
$ =2 {\frac{t^{2}}{2}}_2^4= {t^{2}}_2^4=12 $
$ \Rightarrow i_{rms}=\sqrt{\overline{i^{2}}}=\sqrt{12}=2\sqrt{3}\ A $
