A series LCR circuit is connected to an a.c. source 200 V, 50 Hz. The voltages acorss the resistor, indcutor and capacitor are respectively 200 V, 250 V and 250 V. (i) The algerbriac sum of the three voltages is greater than the source voltage. How is the paradox resolved ? (ii) If `R = 40 Omega`, calculate the current in the circuit.

A series LCR circuit is connected to an a.c. source 200 V, 50 Hz. The

1.	A series LCR circuit is connected to an a.c. source 200 V, 50 Hz. The voltages acorss the resistor, indcutor and capacitor are respectively 200 V, 250 V and 250 V. (i) The algerbriac sum of the three voltages is greater than the source voltage. How is the paradox resolved ? (ii) If `R = 40 Omega`, calculate the current in the circuit.
Answer» Here, `E_(v) = 200 V, v = 52 Hz,` `V_(R ) = 200 V, V_(C ) = 250 V, V_(L) = 250 V` Now, `V_(R ) + V_(C ) + V_(L) = 200 + 250 + 250` `= 700 V`, which is greater than the source voltage 200 V. This is because voltages across C and L are in oppsoite phase and canel out. The sum continues to be 200 V, the source voltage. `I_(v) = (E_(v))/(Z) = (E_(v))/(R ) = (200)/(40) = A`

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