Question

A coil a capacitor and an `AC` source of rms voltage `24 V` are connected in series. By varying the frequency of the source, a maximum rms current of 6 A is observed. If coil is connected is at DC batteryof emf 12 volt and internal resistance `4Omega`, then current through it in steady state is

Answer 1

Consider an L-C-R series circuit as shown below

Maximum current will occur at series reactance lt At series resonance , `Z_(min) = R_(max) = 6A`
`implies I_(max) = V/Z_(min) implies 6 = 24/R implies R = 4Omega`
Now , this inductor coil is connected with a battery of emf 12 V
and internal resistance `4Omega`

In DC circuit , inductor offers zero resistance ,
`therefore current, I = 12/(4 + 4) = 1.5A`