91影视

An inductor is a passive two-terminal device that stores energy in a magnetic field when current passes through it. An inductor stores the energy in form of magnetic field.

A capacitor is a device consisting of two conductors in close proximity that are used to store electrical energy. A capacitor stores energy in form of electric field.

An LC-circuit can store energy while oscillating at its natural resonant frequency. For such circuits, the energy in the circuit shifts between electric and magnetic fields. The angular frequency of this oscillation is given by

$蝇=2\mathrm{蟺}饾憮=\frac{1}{\sqrt{\mathrm{LC}}}$

We are given,

Minimum capacitance of variable capacitor, C = 4.18 pF

Frequency of oscillation, f = 1600 x 10³ Hz

Self-Inductance of a toroidal solenoid is given by

$$\begin{gathered} 鈫�蝇=2蟺饾憮=\frac{1}{\sqrt{LC}} \\ 鈫�L=\frac{1}{4{蟺}^2{饾憮}^{2}C} \\ 鈫�L=\frac{1}{4{蟺}^2{\left(1600*1000\right)}^2\left(4.18*{10}^{-12}\right)} \\ 鈫�L=2.37饾懃{10}^{-3}H \\ 鈫�L=2.37mH \end{gathered}$$

Therefore, the inductance of the coil is 2.37 milli-henry.

Maximum capacitance at the given minimum frequency is

$$\begin{gathered} 鈫�蝇=2蟺饾憮=\frac{1}{\sqrt{LC}} \\ 鈫�C=\frac{1}{4{蟺}^2{饾憮}^{2}L} \\ 鈫�C=\frac{1}{4{蟺}^2{\left(5.40*{10}^{5}Hz\right)}^2\left(2.37*{10}^{-3}H\right)} \\ 鈫�C=3.67饾懃{10}^{-11}H \\ 鈫�C=3.67pF \end{gathered}$$

Therefore, the maximum capacitance of the capacitor is 36.7 pF.