Question

To construct an oscillating LC system, you can choose from a 10 mH inductor, a 4.4 μF capacitor, and a 1.9 μF capacitor. What are the (a) smallest, (b) second smallest, (c) second largest, and (d) largest oscillation frequency that can be set up by these elements in various combinations?

Answer 1

w = angular frequency

w = sqrt (1/LC)

w = 2*pi*f

f = 1/(2*pi*sqrt (LC))

Case A.

L = 10 mH

C = 4.4 uF

f = 1/(2*pi*sqrt (10*10^-3*4.4*10^-6)) = 758.74 Hz

Case B.

L = 10 mH

C = 1.9 uF

f = 1/(2*pi*sqrt (10*10^-3*1.9*10^-6)) = 1154.63 Hz

Case C.

L = 10 mH

C1 = 4.4 uF and C2 = 1.9 uF

C1 and C2 are in parallel circuit

Ceq = C1 + C2 = 4.4 + 1.9 = 6.3 uF

f = 1/(2*pi*sqrt (10*10^-3*6.3*10^-6)) = 634.09 Hz

Case D.

L = 10 mH

C1 = 4.4 uF and C2 = 1.9 uF

C1 and C2 are in series circuit

Ceq = C1*C2/(C1 + C2)

Ceq = 4.4*1.9/(4.4 + 1.9) = 1.33 uF

f = 1/(2*pi*sqrt (10*10^-3*1.33*10^-6)) = 1380.04 Hz

SO ANswer will be

Smallest frequency = 634.09 Hz

second smallest = 758.74 Hz

second largest = 1154.63 Hz

Largest = 1380.04 Hz