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Q.

Resonance occurs in a series LCR circuit when the frequency of the applied emf is 1000 Hz.

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a

at only resonance the voltages across L and C differ in phase by 180o

b

when frequency = 900 Hz, then the current through the voltage source will be ahead of emf of the source

c

the impedance of the circuit is minimum at f = 1000 Hz

d

if the value of C is doubled, resonance occurs at f = 2000 Hz

answer is A, B.

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Detailed Solution

(f=900Hz)<fresonance =1000Hz,    XC>XL and the circuit becomes capacitive and current leads emf at frequency of 900 Hz.
At resonance, impedance is minimum (Z=R).
Not only at resonance, but at all conditions voltages across L and C differ in phase by 180o when connected in series.

fresonance1C. Therefore when C is doubled, the resonance frequency will decrease, i.e., will be at a frequency less than 1000 Hz.

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Resonance occurs in a series LCR circuit when the frequency of the applied emf is 1000 Hz.