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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
- a)f/2
- b)f/4
- c)8f
- d)f/2√2
Correct answer is option 'D'. Can you explain this answer?
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A transistor-oscillator using a resonant circuit with an inductor L (o...
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When a transistor oscillator using a resonant circuit with an inductor L and a capacitor C in series produces oscillations of frequency f, the frequency is determined by the equation:
f = 1 / (2π√(LC))
If L is doubled and C is changed to 4C, the new frequency can be calculated as follows:
New frequency (f') = 1 / (2π√(2L)(4C))
Simplifying this equation:
f' = 1 / (2π√(8LC))
Since 8LC = 8(1/4) = 2, the equation can be further simplified to:
f' = 1 / (2π√2√(LC))
Comparing this with the original equation, we can see that the new frequency is equal to the original frequency divided by the square root of 2:
f' = f / √2
Therefore, the new frequency is f divided by the square root of 2, which can be written as:
f' = f / √2 ≈ f / 1.414
So, the correct answer is (a) f/2.
f = 1 / (2π√(LC))
If L is doubled and C is changed to 4C, the new frequency can be calculated as follows:
New frequency (f') = 1 / (2π√(2L)(4C))
Simplifying this equation:
f' = 1 / (2π√(8LC))
Since 8LC = 8(1/4) = 2, the equation can be further simplified to:
f' = 1 / (2π√2√(LC))
Comparing this with the original equation, we can see that the new frequency is equal to the original frequency divided by the square root of 2:
f' = f / √2
Therefore, the new frequency is f divided by the square root of 2, which can be written as:
f' = f / √2 ≈ f / 1.414
So, the correct answer is (a) f/2.
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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 bea)f/2b)f/4c)8fd)f/2√2Correct answer is option 'D'. Can you explain this answer?
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