A Hartley oscillator uses L1 = 2 mH and L2 = 1.5 mH. The range of capacitance so that the frequency of oscillation can be varied between 1000 kHz to 2000 kHz are:

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  1. Cmax = 7.2 pF and Cmin = 1.8 pF
  2. Cmax = 9.2 pF and Cmin = 0.8 pF
  3. Cmax = 7.2 pF and Cmin = 0.8 pF
  4. Cmax = 9.2 pF and Cmin = 1.8 pF

Answer (Detailed Solution Below)

Option 1 : Cmax = 7.2 pF and Cmin = 1.8 pF
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Detailed Solution

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In Hartley Oscillator,

\(f_0=\frac{1}{2\pi \sqrt{(L_1+L_2)C}}\)

\(C=\frac{1}{4\pi^2f_0^2{(L_1+L_2)}}\)

If f0 = 1000 kHz ⇒ C = 7.2 pF

If f0 = 2000 kHz ⇒ C = 1.8 pF

(or) \(\frac{C_2}{C_1}=\left(\frac{f_{01}}{f_{02}}\right)^2=\frac{1}{4}\)

⇒ \(\frac{C_{max}}{C_{min}}=4\)

This ratio matches with option (a)

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