Question

the instantaneous current in an ac circuit is I = 0.5sin314t what is the rms value of current and frequency of the AC circuit
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Answer 1

Explanation:

$i = asin(ωt + c)$

here, a→current amplitude

c→ phase difference

c=0°

ω=314

$f=ω/2\pi$

f=314/6.28

f=50Hz

$Irms = a \div \sqrt{2}$

Irms =0.5÷√2

Irms=0.353

Answer 2

The rms value of current and frequency of the AC circuit is 0.353 A and 49.97 Hz.

Explanation:

The instantaneous current in an ac circuit is given by :

$I=0.5\ sin(314 t)$

The general equation of ac circuit is given by :

$I=I_o\ sin(\omega t)$

Where

$I_o$ is the peak current

$\omega$ is the angular frequency of the AC circuit

rms value of current is given by,

$I_{rms}=\dfrac{I_o}{\sqrt{2} }$

$I_{rms}=\dfrac{0.5}{\sqrt{2} }$

$I_{rms}=0.353\ A$

The frequency (f) of the AC circuit is given by,

$2\pi f=314$

$f=\dfrac{314}{2\pi}$

f = 49.97 Hz

So, the rms value of current and frequency of the AC circuit is 0.353 A and 49.97 Hz. Hence, this is the required solution.

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