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When a 15 V dc source was applied across a choke coil then a current of 5 Amp flows in it. If the same coil is connected to a 15 V, 50 rad/s ac source a current of 3 Amp flows in the circuit. Determine the inductance of the coil. Also find the power developed in the circuit and its resonance frequency if a 2500 muf capacitor is connected in series with the coil |
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Answer» Solution :coil,`Z=sqrt(R^(2)+omega^(2)L^(2))` `I=(V)/(Z)=(V)/sqrt(R^(2)+omega^(2)L^(2))` For DE SOURCE, `omega = 0` `I=(V)/(R)impliesR=(15)/(5)=3Omegaldots|(i)` When ac is applied`I=(V)/(Z)` i.e.`Z=(15)/(3.0)=5Omega` `thereforeR^(2)+X_(L)^(2)=25` `X_(L)^(2)=25-9=16OmegaimpliesX_(L)=4Omega` `L=(4)/(40)=0.08Henry` Now when the CAPACITOR is connected is series`thereforeX_(C)=(1)/(omegaC)=(1)/(50xx2500xx10^(-6))=8Omega` `Z=sqrt(R^(2)+(X_(L)-X_(c))^(2))=sqrt(3+(48)^(2))=5Omega` `therefore`I=(15)/(5)=3A` `therefore ` `P_(av)=V_(RMS)I_(rms)COSPhi=I_(rmms)^(2)R=(3)^(2)xx3=27W` Resonance frequency f`f=(1)/(2pisqrt(LC))` `=(1)/(2pisqrt((0.08)xx2500xx10^(-6)))=(1000)/(2pixx5xx2sqrt2)` `(25sqrt2)/(pi)=11.25Hz` |
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