When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit

When a capacitor is introduced in series with an LR circuit, forming an LCR circuit, the total impedance is modified.

The impedance of the original LR circuit is $Z_{LR} = \sqrt{R^2 + X_L^2}$, with $X_L = \omega L$.

For the LCR circuit, the impedance becomes $Z_{LCR} = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_C = 1/(\omega C)$.

Since $(X_L - X_C)^2 \le X_L^2$ in most practical cases, the impedance generally decreases: $Z_{LCR} \le Z_{LR}$.

As the current is inversely proportional to impedance, $I = V/Z$, the alternating current increases.

The current is maximized at resonance when $X_L = X_C$, but in general, it increases with the addition of the capacitor.