Question

The resonant frequency of a LC circuit in Hertz whose inductance is 20 μH and capacitance is 80 µF is
1. 128.42  × 104 Hz
2. 6.68 × 104 Hz
3. 3.92 × 104 Hz
4. 6 × 104 Hz

Answer 1

Correct Answer - Option 3 : 3.92 × 104 Hz

CONCEPT:

• LC Circuit: The circuit containing both an inductor (L) and a capacitor (C) can oscillate without a source of emf by shifting the energy stored in the circuit between the electric and magnetic fields is called the LC circuit.
• The tuned circuit has a very high impedance at its resonant frequency.
• The frequency of oscillations generated by the LC circuit entirely depends on the values of the capacitor and inductor and their resonance condition.
• It can be expressed as:

\(⇒ f = \frac{1}{2\pi \sqrt{LC}}\)

Where L = Inductor and C = capacitor

• Frequency (f): The number of oscillations or the number of waves passes a given point in one sec.
• Its SI unit is Hertz.​

EXPLANATION:​

Given - L = 20 μH = 20 × 10^-6 H and C = 80 µF = 80 × 10-6 F

• The resonant frequency of an LC circuit is

\(⇒ f = \frac{1}{2\pi \sqrt{LC}}\)

\(⇒ f = \frac{1}{2×3.14×\sqrt{20×80×10^{-12}}}=\frac{10^6}{40× 2 × 3.14}=0.0392× 10^6\, Hz\)

⇒ 3.92 × 10⁴ Hz

Hence option (3) is correct.