In `LCR` circuit at resonance current in the circuit is `10 sqrt(2) A`. If tnow frequency of the source is changed such that now current lags by `45^(@)` that applied voltage in the circuit . Which of the following is correct.

Options

A. Frequency must be increased and current after the change is `10 A`
B. Frequency must be decreases and current after the change is `10 A`
C. Frequency must be decreased and current is same as that of initial value
D. The given information is insufficient to conclude anything

Answer

A

Explanation

At resonance `X_(L) = X_(C )` in `LCR` circuit at resonance current
`I_("rms") = (V_("rms"))/(R ) = 10 sqrt(2)` ….(i)
When current lags by `(pi)/(4) : (R = X)`
`I_("rms") = (V_("rms"))/(sqrt(R^(2) + X^(2))) (V_("rms"))/(sqrt(2) R) = 10 A`