Physics 2021 JAMB Past Questions - Question 11: The inductance of a turning circuit of Am radio is 4mH. Find the capacitance of the circuit required for reception at 1,200kHz

Correct Answer

B

Explanation

To find the capacitance required for reception at 1,200kHz, we can use the formula for the resonant frequency of an LC circuit:

f = 1 / (2π√(LC))

Where:
f = frequency in hertz (Hz)
L = inductance in henrys (H)
C = capacitance in farads (F)
π is a mathematical constant, approximately equal to 3.14159

Given:
L = 4mH = 4 x 10^-3 H
f = 1,200kHz = 1,200 x 10^3 Hz

We can rearrange the formula to solve for C:

C = 1 / (4π^2f^2L)

Now we can plug in the values:

C = 1 / (4 * π^2 * (1,200 x 10^3)^2 * 4 x 10^-3)

C ≈ 1 / (4 * 9.8696 * 1.44 x 10^12 * 4 x 10^-3)

C ≈ 1 / (157.9136 x 10^9)

C ≈ 6.32 x 10^-12 F

So, the capacitance of the circuit required for reception at 1,200kHz is approximately 6.32 picofarads (pF).