A 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

CONCEPT:

Frequency of Oscillations in an LC Circuit

• The frequency of oscillations in a resonant LC circuit is given by the formula:

f = 1 / (2π√(LC))

where:

• f is the frequency of oscillation
• L is the inductance
• C is the capacitance

EXPLANATION:

• Initially, the frequency of the oscillator is given by:

f = 1 / (2π√(LC))

• When the inductance L is doubled and the capacitance C is changed to 4C, the new frequency f' is given by:

f' = 1 / (2π√(2L * 4C)) = 1 / (2π√(8LC))

Now, factor out the 8:

f' = 1 / (2π√(8)√(LC))

Since √8 = 2√2, we have:

f' = 1 / (2π * 2√2 * √(LC)) = 1 / (2√2 * 2π√(LC))

Therefore:

f' = f / (2√2)

Therefore, the correct answer is option 2: f / 2√2.