What is the period of oscillation of an LC circuit consistin

What is the period of oscillation of an LC circuit consisting of a 1.9-mH coil and a 19-mu F capacitor? ms A circuit that oscillates consists solely of an 84-mu F capacitor and a variable ideal inductor. What inductance is needed in order to tune this circuit to oscillate at 50 Hz? mH

Solution

Here ,

a)

L = 0.0019 H

C = 19 uF

period of oscillation = 2pi * sqrt(L * C)

period of oscillation = 2pi * sqrt(0.0019 * 19 *10^-6)

period of oscillation = 1.194 *10^-3 s = 1.194 ms

b)

for f = 50 Hz , let the inductance is L

f = 1/(2pi * sqrt(L*C))

50 * 2pi = 1/(sqrt(84 *10^-6 * L))

solving for L

L = 0.120 H

L = 120 mH

the inductance needed is 120 mH