In an AC circuit, the instantaneous current is given by I = 10 sin(314t + pi/3) amperes. What is the RMS value of the current and the frequency of the AC source?

A. 7.07 A, 50 Hz — The peak current is 10 A, so the RMS current is 10/sqrt(2) which is approximately 7.07 A. The angular frequency omega is 314 rad/s, so frequency f = 314/(2*pi) which is approximately 50 Hz.

JEE Main · PhysicsHard

$In an AC circuit, the instantaneous current is given by I = 10 sin (314 t + π /3) amperes. What is the RMS value of the current and the frequency of the AC source?$

A. $7.07 A, 50 Hz$
B. $10 A, 100 Hz$
C. $7.07 A, 100 Hz$
D. $14.14 A, 50 Hz$

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Correct answer: A — $7.07 A, 50 Hz$

Solution

The peak current I_{0} = 10 A, so I_{r m s} = 10/ 2 \approx 7.07 A . The angular frequency ω = 314 rad/s, so f = 314/ (2 π) \approx 50 Hz .

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In an AC circuit, the instantaneous current is given by I=10sin(314t+π/3) amperes. What is the RMS value of the current and the frequency of the AC source?

Solution

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More AC Circuits practice questions

$In an AC circuit, the instantaneous current is given by I = 10 sin (314 t + π /3) amperes. What is the RMS value of the current and the frequency of the AC source?$