alternating-currents Question 1
Question: Q. 1. If the $r m s$ current in a $50 \mathrm{~Hz} \mathrm{AC}$ circuit is $5 \mathrm{~A}$, the value of the current $1 / 300 \mathrm{~s}$ after its value becomes zero is (a) $5 \sqrt{2} A$. (b) $5 \sqrt{\frac{3}{2}} \mathrm{~A}$. (c) $\frac{5}{6} \mathrm{~A}$. (d) $\frac{5}{\sqrt{2}} A$.
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Solution:
Ans. Correct option : (b) Explanation :
Here, $I_{\mathrm{rms}}=5 \mathrm{~A}, \mathrm{v}=50 \mathrm{~Hz}$ and $\mathrm{L}=\frac{1}{300} \mathrm{~s}$
$$ I_{0}=\text { Peak value }=\sqrt{2} I_{r m s}=\sqrt{2} \times 5=5 \sqrt{2} \mathrm{~A} $$
Now, $I=I_{0} \sin \omega t=5 \sqrt{2} \sin 2 \pi v t$
$$ =5 \sqrt{2} \sin 2 \pi \times 50 \times \frac{1}{300}=5 \sqrt{\frac{3}{2}} \mathrm{~A} $$
