A transistor-oscillator using a resonant circuit with an inductor L ( of negligible resistance ) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be
Question
A transistor-oscillator using a resonant circuit with an inductor L ( of negligible resistance ) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be
Solution
The frequency of oscillation in a LC circuit is given by the formula:
f = 1 / (2π √(LC))
Where:
- f is the frequency
- L is the inductance
- C is the capacitance
If L is doubled and C is changed to 4C, the new frequency f' will be:
f' = 1 / (2π √(2L * 4C))
Simplifying this gives:
f' = 1 / (2π √(8LC))
We can see that the new frequency is half the original frequency. Therefore, if L is doubled and C is changed to 4C, the frequency will be halved.
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