• question_answer Figure shows a conducting horizontal rod of resistance r is made to oscillate simple harmonically with a fixed amplitude in a uniform and constant magnetic field B, directed inwards. The ends of rod always touch two parallel fixed vertical conducting rails. The ends of rails are joined by an inductor and a capacitor having self inductance and capacitance $\frac{1}{\pi }$ Henry and $\frac{1}{\pi }$ farad respectively. The amplitude of current in the circuit depends on the frequency of oscillation of rod. The amplitude of the current will be maximum when the time period of rod is: (do not consider self inductance anywhere other than in the inductor) A) 0.5 sec B) 1 sec C) 2 sec     D)  4 sec

Here oscillating rod is an ac source because emf induced in it is $(vB\ell )\,\,;$ which varies sinusoidally because v varies sinusoidally. Maximum current will flow through the circuit under resonance condition. Therefore time period of oscillation of rod is $T=2\pi \sqrt{LC}=2\sec .$
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