Question

A radio can tune over the frequency range of a portion of MWbroadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effectiveinductance of 200 μH, what must be the range of its variable capacitor?[Hint: For tuning, the natural frequency i.e., the frequency of freeoscillations of the LC circuit should be equal to the frequency of theradiowave.]

Answer 1

Given: A radio can tune over the range of frequencies from 800 kHz to 1200 kHz and the inductance of its LC circuit is 200 μH.

The capacitance of variable capacitor is given as,

C= 1 ω 2 L = 1 ( 2πf ) 2 ×L

Where, the frequency is f and inductance of radio is L.

By substituting the values for the lower tuning frequency, we get

C l = 1 ( 2π×800× 10 3 ) 2 ×200× 10 −6 =198 pF

By substituting the values for the upper tuning frequency, we get

C u = 1 ( 2π×1200× 10 3 ) 2 ×200× 10 −6 =88 pF

Thus, the range of capacitor is 88 pF to 198 pF.