A Series L-C-R circuit Having L = 1.5 H,  is Connected To A 200-V a.c. Supply Of Variable Frequency. When The Supply Frequency Equals The Natural Frequency Of The Circuit, Find The Average Power Transferred To The Circuit In One Full Cycle. 

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A series L-C-R circuit having L = 1.5 H,  is connected to a 200-V a.c. supply of variable frequency. When the supply frequency equals the natural frequency of the circuit, find the average power transferred to the circuit in one full cycle. 


Correct option is

2000 W

The natural (angular) frequency of the L-C-R circuit is 


When an a.c. voltage of angular frequency  = 138 Hz is applied to the circuit, we have 


and capacitive reactance, 




This is the condition of resonance. The rms resonant current in the circuit is  


The power is transferred to the resistor only. Therefore  




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