In a series LCR circuit, obtain the conditions under which (i) the impedance of the circuit is minimum , and (ii) wattless current flows in the circuit.

Explanation

Impedance of series LCR circuit is given by `Z = sqrt(R^(2) + (X_(L) - X_(C))^(2)`
or for Z to be minimum, `X_(L) = X_(C)` (or `omega = (1)/(sqrt(LC))`)
For wattless current to flow circuits should not have any ohmic resistance i.e., R = 0
Alternatively : Power `= V_(rms)I_(rms) cos phi`
for `phi = 90^(@) = pi//2`
Power = 0
`:.` Wattless current flows when the impedance of the circuit is purely inductive / capacitive of the combination of the two.