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A current of 4 A flows in a coil when it...

A current of 4 A flows in a coil when it is connected to a 12V dc source. When the same coil is connected to an a.c. source (12 V, 8 Hz), a current of 2.4 A flows in the coil. Calculate coefficient of self inductance (L) of the coil.

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Given : Current of 4 A flow in coil when connected to 12 V d.c. source.
Current of 2.4 A flow in coil when connected to 12 V, 8 Hz a.c. source.
We know,
`V=L_(dc)R`
`12=4xxR`
`R=3Omega`
When the coil is connected to a.c, source,
`I_(ac)=(E)/(Z)`
`2.5=(12)/(Z)`
`Z=5Omega`
But `Z=sqrt(R^(2)+X_(L)^(2))`
`5=sqrt(3^(2)+X_(L)^(2))`
`impliesX_(L)=4Omega`
But `X_(L)=2pifL`
`:.4=2pixx8xxL`
`impliesL=0.0796H`
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