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(a) An AC source of voltage V = V_(0) sin omegat is connected across a series combination of an inductor a capacitor and a resistor . Use the phasor diagram to obtain the expression for the impedance of the circuit and phase angle between the voltage and the current. (b) A capacitor of unknown capacitance a resistor of 100 Omega and an inductor of self - inductance L = (4 //pi^(2)) henry are in series connected to an AC source of 200 V and 50 Hz . Calculate the value of the capacitance and the current that flows in the circuit when the current is in phase with the voltage . |
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Answer» Solution :(b)R =100 `Omega` L = `(4)/(pi^(2)) , f = 50 `Hz, `epsilon = 200` V the circuit is in PHASE with voltage. Therefore, `X_(L) = X_(C)`,Z = R ` 2 pi f L = (1)/(2 pi f C)` C = `(1)/(4 pi^(2) f^(2) L) = (1 xx (3.14)^(2))/(4 (3.14)^(2)(50)^(2) xx 4) = 25 mu` F `I_(rms) = (epsilon_(rms))/(R) = (200)/(100) = 2 A ` |
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