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 .

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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