A resonant circuit using a 286-nFnF capacitor is to resonate at 18.0 kHzkHz. The air-core inductor is to be a solenoid with closely packed coils made from 12.0 mm of insulated wire 1.1 in diameter. The permeability of free space is 4π×10−7T⋅m/A4π×10−7T⋅m/A.

How many loops will the inductor contain?

The inductor contains loops  

Explanation:

From the question we are told that

     The capacitance of the capacitor is  

      The resonance frequency is  

       The diameter is  

       The  of the air-core inductor is

        The permeability of free space is  

Generally the inductance of this air-core inductor is mathematically represented as

This inductance can also be mathematically represented as

Where is the angular speed mathematically given as

So

Now equating the both formulas for inductance

making N the subject of  the formula

 Substituting value

              loops  

an obstruction