An AC source produces an alternating current in a circuit with the function $i\left(t\right)=\left(1.5A\right)\cos\left\lbrack\left(250s^{-1}\right)t\right\rbrack$. What is the frequency of the source? What is the maximum current in the circuit?

• A. f=39.3 Hz
• B. f=250 Hz
• C. f=393 Hz
• D. f=1570 Hz

Answer: (A)

Verified step by step guidance

1. Identify the given function for the alternating current: i(t) = (1.5 A) cos[(250 s^{-1}) t].
2. Recognize that the function is in the form i(t) = I_0 cos(ωt), where I_0 is the maximum current and ω is the angular frequency.
3. Determine the maximum current, I_0, from the function. Here, I_0 = 1.5 A.
4. Identify the angular frequency, ω, from the function. Here, ω = 250 s^{-1}.
5. Use the relationship between angular frequency and frequency: ω = 2πf, to solve for the frequency, f. Rearrange to find f = ω / (2π).