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?

Answer:

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.