An alternating current is represented by the equation, i=100 2 sin ⁡ (100 πt ) ampere. The RMS value of current and the frequency of the given alternating current are

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Correct answer: D. (d) To solve the problem, we need to determine both the RMS value of the current and the frequency from the given equation: i (t )=100 2 sin ⁡ (100 πt ) . Here's how we do it step by step: RMS Current Calculation: For a sinusoidal current of the form i (t )=I_0 sin ⁡ ( ωt ), the RMS (root-mean-square) current is given by: I_ RMS= I_0 2 . In our case, the amplitude I_0=100 2 A. Plugging into the formula: I_ RMS= 100 2 2=100 A . Frequency Calculation: The argument of the sine function is 100 πt. In the general form sin ⁡ ( ωt ) , is the angular frequency which relates to the frequency f by the equation: =2 πf . Given =100 , we can solve for f : f= 2 = 100 2 =50 Hz With these calculations, we find that the RMS current is 100 A and the frequency is 50 Hz.

$An alternating current is represented by the equation, i = 1002 sin (100 πt) ampere. The RMS value of current and the frequency of the given alternating current are$

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