For an RLC circuit driven with voltage of amplitude $v_{\mathrm{m}}$ and frequency $\omega_{\mathrm{o}}=\frac{1}{\sqrt{\mathrm{LC}}}$ the current exibits resonance. The quality factor, Q is given by :

(B) $\frac{\omega_{\mathrm{o}} \mathrm{L}}{\mathrm{R}}$

(A) $\frac{\mathrm{CR}}{\omega_{\mathrm{o}}}$

(C) $\frac{\omega_{\mathrm{O}} \mathrm{R}}{\mathrm{L}}$

(D) $\frac{\mathrm{R}}{(\omega_{\mathrm{o}} \mathrm{C})}$

JEE Main · 2018 · 08 Apr 2018 · Offline · Alternating Current

For an RLC circuit driven with voltage of amplitude

v_{m}

and frequency

ω_{o} = \frac{1}{LC}

the current exibits resonance. The quality factor, Q is given by :

Answer: (B)

At resonance the sharpness of an RLC circuit is measured by its quality factor, the inductor's resonant reactance compared with the resistance,

Q = \frac{ω _{0} L}{R}

, which with

ω_{0} = \frac{1}{L C}

can also be written

Q = \frac{1}{R} \frac{L}{C}

. A quick check settles the choice, since of the forms offered only

\frac{ω _{0} L}{R}

is dimensionless as a quality factor must be, giving

Q = \frac{ω _{0} L}{R}

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option