A current of `4A` flows in a coil when connected to a `12V DC` source. If the same coil is connected to a `12V, 50 rad//s AC` source, a current of `2.4A` flows in the circuit. Determine the inductance of the coil. Also, find the power developed in the circuit if a`2500muF` capacitor is connected in series with the coil.

Options

A. `(pi/sqrt3)H`
B. `(sqrt3/pi)H`
C. `(2/pi)H`
D. none of these

Answer

B

Explanation

`I_(DC)=V_(DC)/R`
`I=100/RimpliesR=100Omega`
`I_(AC)=V_(AC)/(sqrt(R^2+X_L^2))`
`0.5=100/(sqrt((100)^2+X_L^2))`
or `X_L=100sqrt3Omega=(2pifL)`
`:. L=(100sqrt3)/(2pif)=(100sqrt3)/(2pi(50))`
`=(sqrt3/pi)H`