A series combination of resistor of resistance $100 ~\Omega$, inductor of inductance $1 ~\mathrm{H}$ and capacitor of capacitance $6.25 ~\mu \mathrm{F}$ is connected to an ac source. The quality factor of the circuit will be __________

<p>The Q factor (quality factor) in a series RLC circuit can be given by the formula: </p> <p>$ Q = \frac{X_L}{R} = \frac{\omega L}{R} $</p> <p>where ($X_L$) is the inductive reactance, (R) is the resistance, (L) is the inductance, and ($\omega$) is the angular frequency. </p> <p>In a series RLC circuit at resonance, the resonant frequency (f) is given by</p> <p>$ f = \frac{1}{2\pi\sqrt{LC}} $</p> <p>or equivalently, the angular frequency ($\omega$) at resonance is </p> <p>$ \omega = \frac{1}{\sqrt{LC}} $</p> <p>Substituting (L = 1H) and ($C = 6.25 \mu F = 6.25 \times 10^{-6} F$) into the equation for (\omega) gives</p> <p>$\omega = \frac{1}{\sqrt{1H \times 6.25 \times 10^{-6}F}}$ = 400 rad/s</p> <p>Substituting ($\omega = 400 rad/s$), (L = 1H), and ($R = 100\Omega$) into the equation for the Q factor gives</p> <p>$ Q = \frac{\omega L}{R} = \frac{400 rad/s \times 1H}{100\Omega} = 4 $</p> <p>So, the Q factor of the circuit is 4.</p>