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 RMS current is calculated by dividing the peak current by the square root of two, and the frequency is derived from the angular frequency component of the current equation.

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. $14.14 A, 50 Hz$

Show correct answer & step-by-step solution

Correct answer: A — $7.07 A, 50 Hz$

Solution

$The given instantaneous current is I = 10 sin (314 t + π /3), where the peak current I_{0} = 10 A and the angular frequency ω = 314 rad/s .$
$Calculate the RMS current using the formula I_{r m s} = \frac{I _{0}}{2} = \frac{10}{1.414} \approx 7.07 A .$
$Calculate the frequency using the relation f = \frac{ω}{2 π} = \frac{314}{2 \times 3.14} \approx 50 Hz .$
$Hence the answer is (A).$

Attempt this question & track your score

Attempt & Track Free →

More AC Circuits practice questions

$An alternating current is given by the equation I = 10 sin(314t). What is the frequency of this current in Hertz?$
$In a pure resistive AC circuit, what is the phase difference between the voltage and the current?$
$What is the inductive reactance of an inductor of 0.1 Henry at a frequency of 50 Hertz?$
$T h er oo t m e an s q u a r e v a l u eo f ana l t er na t in g c u r r e n t i sr e l a t e d t o t h e p e ak c u r r e n t I_{0} b y w hi c h f or m u l a ?$
$In a series LCR circuit at resonance, what is the power factor of the circuit?$
$In an LCR series circuit, the resonance frequency is f. If the capacitance is made 4 times its initial value, what will$
$A resistor of 10 ohms and an inductor of 0.1 H are connected in series to a 50 V, 50 Hz AC source. What is the phase ang$
$An AC voltage V = 100 sin(100t) is applied to a capacitor of 1 microfarad. What is the peak current in the circuit?$
$In an AC circuit, the voltage and current are given by V = 100 sin(100t) and I = 100 sin(100t + pi/3). What is the power$
$An AC source with voltage V = V0 sin(omega t) is connected to a series LCR circuit. If the frequency of the source is va$
$In an LCR series circuit, the resonance frequency is f0. If the capacitor is replaced by two capacitors of the same capa$
$A series LCR circuit is connected to an AC voltage source. At resonance, the voltage across the inductor is 100V. If the$

View all AC Circuits questions →

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

Attempt this question & track your score

More AC Circuits practice questions

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