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

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 quality factor of this resonator is . [π=3.14] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Given: L =2 × 10-4 H R =6.28 Ω f =10 MHz =107 Hz Since quality factor, Q =ω0 ( L / R )=2 π f ( L / R ) ∴ Q =2 π × 107 × (2 × 10-4/6.28) Q =2 × 103=2000

Q. A resonance circuit having inductance and resistance $2 \times 1 0^{- 4} H$ and $6.28Ω$ respectively oscillates at $10 M Hz$ frequency. The value of quality factor of this resonator is ________. $[π = 3.14]$

Given : $L = 2 \times 1 0^{- 4} H$
$R = 6.28Ω$
$f = 10 M Hz = 1 0^{7} Hz$
Since quality factor,
$Q = ω_{0} \frac{L}{R} = 2 π f \frac{L}{R}$
$∴ Q = 2 π \times 1 0^{7} \times \frac{2 \times 1 0 ^{- 4}}{6.28}$
$Q = 2 \times 1 0^{3} = 2000$

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

Given : L=2×10−4H R=6.28Ω f=10MHz=107Hz Since quality factor, Q=ω0​RL​=2πfRL​ ∴Q=2π×107×6.282×10−4​ Q=2×103=2000

Q. A resonance circuit having inductance and resistance $2 \times 1 0^{- 4} H$ and $6.28Ω$ respectively oscillates at $10 M Hz$ frequency. The value of quality factor of this resonator is ________. $[π = 3.14]$

Given : $L = 2 \times 1 0^{- 4} H$
$R = 6.28Ω$
$f = 10 M Hz = 1 0^{7} Hz$
Since quality factor,
$Q = ω_{0} \frac{L}{R} = 2 π f \frac{L}{R}$
$∴ Q = 2 π \times 1 0^{7} \times \frac{2 \times 1 0 ^{- 4}}{6.28}$
$Q = 2 \times 1 0^{3} = 2000$