Network Theory Test 4

Result

Network Theory Test 4

Score
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Question 1
1 / -0

The output frequency of an LC tank oscillator circuit employing a capacitive sensor acting as a capacitor of the tank is 100 kHz. If the sensor capacitance increases by 10% the output frequency becomes ________ kHz.

A
95-96

B
954-961

C
957-966

D
959-962

Solution

The frequency of oscillation is equal to the resonance frequency of the tank circuit is:
\({f_1} = \frac{1}{{2\pi \sqrt {L{C_1}} }}\) ---(1)
The capacitance is increased by 10%, i.e.
⇒ C₂ = C₁+ 0.1 C₁
C₂ = 1.1 C₁
New resonant frequency will be:
\({f_2} = \frac{1}{{2\pi \sqrt {L{C_2}} }}\)
\(f_2= \frac{1}{{2\pi \sqrt {1.1L{C_1}} }}\) ---(2)
Dividing Equation (2) with (1), we get:
\(\frac{f_2}{f_1}=\frac{1}{\sqrt{1.1}} \)
With f₁ = 100 kHz, f₂ is:
f₂ = 95.346 KHz