InterviewSolution
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InterviewSolution
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Derive an expression for the impedance of a series LCR circuit connected to an a.c. supplied to the of variable frequency. Plot a graph showing variation of current with the frequency of the applied voltage. Explain briefly how the phenomenon of resonance in the circuit can be used in the turning mechanism of a radio or TV set. |
Answer» Solution : Let `V_(L), V_(R ), V_(C )` and V represent the VOLTAGE across the inductor resistor capacitor and the source respectively. `V_(R )`is parallel to I. `V_(C )` is `pi//2`behind I and `V_(L)` is `pi//2` ahead of I. Now `V_(OR) = V_(OC) = i_(0)X_(C)` and `V_(OL) = I_(0)X_(L)` CLEARLY `V_(0)^(2) = V_(OR)^(2) + (V_(OL) - V_(OC))^(2)` `= i_(0)^(2)[R^(2) + (X_(L) - X_(C))^(2)]` Thus `i_(0) = (V_(0))/(sqrt(R^(2) + (X_(L) - X_(C))^(2))` Impedance `= (V_(0))/(i_(0)) = sqrt(R^(2) + (X_(L) - X_(C))^(2))` `= sqrt(R^(2) + (omega L - (1)/(omega C))^(2))`  The capacitance of a capacitor in the turning circuit is varied such that the reason and frequency of the circuit becomes nearly EQUAL to the frequency of the radio signal to be received. When this happens the amplitude of the CURRENT becomes MAXIMUM in the receiving circuit. |
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