The frequency of an LC oscillator is f0 The inductor is in t

The frequency of an LC oscillator is f₀. The inductor is in the form of a long solenoid with radius a, length , and many turns N (with

>>1

). If the solenoid is stretched to a new length 2 while keeping a and N constant, what is the new frequency of oscillations of the oscillator?

Solution

Frequnce of LC oscillator f= 1/(2*pi) * 1/(LC)^1/2

now L directly proportional to length in solenoid now if length is increased 2 times inductance would be 2 times

so frequency would be (1/2)^1/2 times