Physics 2002 JAMB Past Questions - Question 50: At what frequency would a capacitor of 2.5μF used in radio circuit that have a resistance of 250Ω.

Correct Answer

E

Explanation

Xc=1/2πFC ;250=1/2π*F*2.5*10-6F=800/π HzThe frequency at which a capacitor and a resistor in an RC circuit affect the behavior of a circuit can be calculated using the formula for the angular frequency, which is given by:

ω = 1 / (RC)

Where:
ω (omega) is the angular frequency in radians per second (rad/s).
R is the resistance in ohms (Ω).
C is the capacitance in farads (F).

In your case:
R = 250 Ω
C = 2.5 μF = 2.5 × 10^(-6) F

Now, you can calculate the angular frequency:

ω = 1 / (250 Ω * 2.5 × 10^(-6) F)
ω = 1 / (250 Ω * 2.5 × 10^(-6) F)
ω = 1 / (625 × 10^(-6) Ω·F)
ω = 1.6 × 10^3 rad/s

Now, to find the frequency (f) in hertz (Hz), you can use the following formula:

f = ω / (2π)

Where:
f is the frequency in hertz (Hz).
ω is the angular frequency in radians per second (rad/s).

f = (1.6 × 10^3 rad/s) / (2π)
f ≈ 254.47 Hz

So, the frequency at which this RC circuit with a 2.5 μF capacitor and a 250 Ω resistor operates is approximately 254.47 Hz.