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(a) An a.c. source of voltage V=V_(m) sin omega tis connected across a series combination of an inductor, a capacitor and a resistor. Use the phasor diagram to obtain the expression for (i) impedance of the circuit, and (ii) phase angle between the voltage and the current (b) A capacitor of unknown capacitor, a resistor of 100 Omegaand an inductor of self-inductance L = 4/pi^(2) H are connected in series to an a.c. 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 :(a) N/A (B) Here, `R = 100 Omega, L = 4/pi^(2) H, V_(rms) = 200V` and v= 50 HZ Since current flowing in the circuit is in phase with voltage, hence resonant frequency `v_(r) =v = 50 Hz`, As `v_(r) = 1/(2pi sqrt(LC))` `THEREFORE C = 1/(4pi^(2) Lv_(r)^(2)) = 1/(4pi^(2) xx (4/pi^(2)) xx (50)^(2)) = 25 xx 10^(-6) F = 25 MUF` and current `I_(rms) = V_(rms)/Z = V_(rms)/R = 200/100 A = 2.0 A` |
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