In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency ω₀. The value of x is :

Solution

Physics sir · 4 steps

Resonant frequency goes as one over the root of LC, so find how much LC grows and take its square root.

1. Resonance formula. In an LC circuit, energy swings between the inductor and the capacitor at the natural angular frequency below.

   ω₀ = 1/√LC

2. New product LC. With L' = 2L and C' = 8C, the product becomes L'C' = 16 LC. So it is 16 times larger.
3. Take the root. ω' = 1/√(16 LC) = 1/4 × 1/√LC = ω₀/4.
4. So. The new resonant frequency is one quarter of the old one, so x = 1/4, option (a).

The idea to keep. Since ω₀ ∝ 1/√LC, multiply the factors on L and C, take the square root, then flip it. Bigger L or C always means slower oscillation.

Answer from the NTA final answer key. Solution by PrepWiser.