Step 1: Understanding the Concept:
The current in an AC circuit depends inversely on the total impedance ($Z$) of the circuit.
An LR circuit has resistance $R$ and inductive reactance $X_L$.
Adding a capacitor introduces capacitive reactance $X_C$, changing it to an LCR series circuit.
Step 2: Key Formula or Approach:
Initial impedance of the LR circuit is:
\[ Z_1 = \sqrt{R^2 + X_L^2} \]
New impedance after adding a capacitor in series is:
\[ Z_2 = \sqrt{R^2 + (X_L - X_C)^2} \]
The AC current is given by $I = \frac{V}{Z}$.
Step 3: Detailed Explanation:
In the original LR circuit, the inductive reactance $X_L$ adds squarely with the resistance $R$ to limit the current.
When a capacitor is connected in series, its reactance $X_C$ opposes the inductive reactance $X_L$ because the voltage across an inductor leads the current by $90^\circ$, while the voltage across a capacitor lags by $90^\circ$ (they are $180^\circ$ out of phase).
Therefore, the net reactive term becomes $(X_L - X_C)$.
As long as the added capacitance is not overwhelmingly small (which would make $X_C$ extremely large), the term $(X_L - X_C)^2$ is generally smaller than $X_L^2$.
Specifically, if $X_C<2X_L$, then $(X_L - X_C)^2<X_L^2$. In practical power factor correction and typical textbook problems of this phrasing, the capacitor is added to compensate for the lagging current, bringing the circuit closer to resonance ($X_L = X_C$).
Because the net reactance decreases, the overall impedance $Z_2$ is less than the initial impedance $Z_1$.
Since $Z$ decreases and $I = V/Z$ (assuming constant source voltage $V$), the current $I$ flowing in the circuit must increase.
Step 4: Final Answer:
The alternating current flowing in the circuit increases.