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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]

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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 = XL / R = ωL / R

also, ω = 2πf, so

⇒ Q = 2πfL / R

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

Q = 2000

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