In the pure inductive circuit, the curves between frequency f and reciprocal of inductive reactance `1//X_(L)` is

Explanation

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`