The voltage across a reactance carrying an a.c. I = 10 sin200πt is given by v = 20 sin (200 \(\pi\)t + \(\frac{\pi}{2}\)), Calculate the frequency.
A
400 Hz
B
200 Hz
C
100 Hz
D
300 Hz
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
The general form of an alternating quantity is A sin(ωt + ϕ), where the angular frequency is ω = 2πf.
I = 10sin200πt, voltage, v = 20sin(200πt+π/2)
From the expressions above, ω = 200π.
But ω = 2πf
f = \(\frac{\omega}{2\pi}\) = \(\frac{200\pi}{2\pi}\) = 100Hz.
Source: WAEC / JAMB / NECO Classroom Archive (Record #78253)