Question

A resonance circuit having inductance and resistance 2 × 10^–4 H and 6.28 Ω respectively oscillates at 10 MHz frequency. The value of the quality factor of this resonator is________. [π = 3.14]

Answer 1

correct answer is 2000 

R = 6.28 Ω

f = 10 MHz

L = 2 × 10^-4 Henry

We know that quality factor Q is given by

⇒ Q = X_L / R = ωL / R

also, ω = 2πf, so

⇒ Q = 2πfL / R

⇒ Q = 2π × 10 × 106 × 2 × 10^-4 / 6.28 = 2000

Q = 2000