The frequency of oscillation of a certain LC circuit is 250kHz. At time t=0, pla

Question

The frequency of oscillation of a certain LC circuit is 250kHz. At time t=0, plate A of the capacitor has maximum positivecharge. At what times t>0 will (a) plate A again have maximum positive charge. (b) the other plate of the capacitor have maximum positivecharge, and (c) the inductor have maximum magnetic field? The frequency of oscillation of a certain LC circuit is 250kHz. At time t=0, plate A of the capacitor has maximum positivecharge. At what times t>0 will (a) plate A again have maximum positive charge. (b) the other plate of the capacitor have maximum positivecharge, and (c) the inductor have maximum magnetic field?

Explanation / Answer

(a) We have the charge on the plateA of the capacitor is q =q0cos(2f t) At t = 0 q = q0 Plate A will have maximum positive charge when cos(2f t)= 1                                                                            or2f t = 2n where n is an integer                                                                            or t = n /f                                  givenf = 250kHz                                            = 250*103Hz Therefore t =  n /( 250*103Hz)                  = 4n*10-6s So at times t = 4s, 8s,12s,...............Plate A will have maximum positivecharge. (b) Other plate of the capacitor will have maximum positive chargeat times t = 2s, 6s,10s,............... (c)The inductor will have maximum magnetic field when thecharge on the capacitor is zero. This will happen when cos(2f t) = 0                            or 2f t = (2n + 1)/2                             ort = (2n+1) / 4f                                   =(2n+1) / (4*250*103Hz)                                  = (2n+1) *10-6s                                  = (2n + 1)s So  the inductor have maximum magnetic field at t =1s, 3s, 5s, 7s, 9s,11s,............... Plate A will have maximum positive charge when cos(2f t)= 1                                                                            or2f t = 2n where n is an integer                                                                            or t = n /f                                  givenf = 250kHz                                            = 250*103Hz Therefore t =  n /( 250*103Hz)                  = 4n*10-6s So at times t = 4s, 8s,12s,...............Plate A will have maximum positivecharge. (b) Other plate of the capacitor will have maximum positive chargeat times t = 2s, 6s,10s,............... (c)The inductor will have maximum magnetic field when thecharge on the capacitor is zero. This will happen when cos(2f t) = 0                            or 2f t = (2n + 1)/2                             ort = (2n+1) / 4f                                   =(2n+1) / (4*250*103Hz)                                  = (2n+1) *10-6s                                  = (2n + 1)s So  the inductor have maximum magnetic field at t =1s, 3s, 5s, 7s, 9s,11s,...............

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