Ncert Exercises & Solutions

If the RMS current in a $50~\text{Hz}$ AC circuit is $5~\text{A}$ , the value of the current $\dfrac{1}{300}~\text{s}$ after its value becomes zero is:

1.	$5\sqrt2~\text{A}$	2.	$5\sqrt{\dfrac32}~\text{A}$
3.	$\sqrt{\dfrac56}~\text{A}$	4.	$\dfrac{5}{\sqrt2}~\text{A}$

(b) Hint : The current varies periodically in the circuit .

$(b) Hint : The current varies periodically in the circuit .$

$Step 1 : Given, ν = 50 Hz, I_{rms} = 5 A$

$t = \frac{1}{300} s$

$We have to find I (t) .$

$Step 2 : I_{0} = Peak value = \sqrt{2} I_{rms} = \sqrt{2} \times 5$

$= 5 \sqrt{2} A$

$Step 3 : I = I_{0} sinωt = 5 \sqrt{2} \sin 2 πνt = 5 \sqrt{2} \sin 2 \times 50 \times \frac{1}{300}$

$= 5 \sqrt{2} \sin \frac{π}{3} = 5 \sqrt{2} \times \frac{\sqrt{3}}{2} = 5 \sqrt{3 / 2} A$

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