• # question_answer What do you understand by "sharpness of resonance" in a series L-C-R circuit? Write expression for Q-factor of the circuit. Or The magnetic flux passing perpendicular to the plane of a coil and directed into the paper is given by $\phi =5{{t}^{2}}+6t+2,$ where $\phi$ is in milliwebers and t in seconds. (i) What is the magnitude of the induced emf set up in the loop, t = 1 s? (ii) What is the direction of current through the resistor R?

Or (i) E = 16 m V The sharpness of resonance is given by $={{\omega }_{0}}/2\Delta \omega$ where, ${{\omega }_{0}}=$ resonance frequency $\Delta \omega =$ bandwidth of the circuit The smaller the $\Delta \omega ,$ sharper or narrower is the resonance. The quality factor Q is defined by $Q=\frac{{{\omega }_{0}}L}{R}=\frac{1}{{{\omega }_{0}}CR}$ Q is an indicator of the sharpness of the resonance. The higher the value of Q, the sharper is the peak value of current. Or             Given, $\phi =5{{t}^{2}}+6t+2\,mWb$             (i) Induced emf, $e=\frac{d\phi }{dt}=(10t+6)\times {{10}^{-3}}Wb$             At $t=1s,$             $e=(10\times 1+6)\times {{10}^{-3}}=1.6\times {{10}^{-2}}V=16mV$ (ii) The direction of induced current is such as to oppose the change in flux. So, the direction of induced current flows through the resistor R from left to right.