Question

A current of 1 A flows in a coll when connected to a 100 V dc source. IF the same coll is connected to a 100 V, 50 Hz ac source, a current od 0.5 A flows in the coll. Calculate the inductance of the coll.

Answer 1

If R be the resistance of the coll, in dc circuit `E/I=R`
or,`R=100/I=100Omega`
In ac circuit , `I_(rms)=(E_(rms))/(sqrt(R^2+(omegaL)^2))`
or,`sqrt(R^2+(omegaL)^2)=(E_(rms))/(I_(rms))=100/0.5=200Omega`
`thereforeR^2+(omegaL)^2=(200)^2`
or,` omegaL=sqrt((200)^2-(100)^2)=100sqrt3Omega`
or,`L=(100sqrt3)/omega=(100times1.732)/(2times3.14times50)=0.55 H`.