The frequency of oscillations produced by the Colpitt's oscillator shown in the figure is (values of components are given): 

Concept:

The circuit diagram of the transistorized Colpitts Oscillator is shown below.

The frequency of oscillations is given by,

\(f = \frac{1}{{2\pi \sqrt {L{C_{eq}}} }}\)

\({C_{eq}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}\)

Calculation:

Given that, L = 100 μH, C1 = 0.001μF , C2 = 0.01μF

\({C_{eq}} = \frac{{0.01 \times {{10}^{ - 6}} \times 0.001 \times {{10}^{ - 6}}}}{{0.01 \times {{10}^{ - 6}} + 0.001 \times {{10}^{ - 6}}}} = 0.909\;nF\)

The frequency of oscillations \(f = \frac{1}{{2\pi \sqrt {100 \times {{10}^{ - 6}} \times 0.909 \times {{10}^{ - 9}}} }} = 527.883\;KHz\)