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]
correct answer is 2000
R = 6.28 Ω f = 10 MHz L = 2 × 10^{-4} Henry
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