In 1847, Kirchhoff proposed his current law and voltage law through the study of complex linear DC circuits. Building on the analysis of transient currents in linear sinusoidal AC circuits, this paper demonstrates that Kirchhoff’s current law can serve as an approximate formula for transient analysis in low- and medium-frequency AC circuits. However, it becomes invalid for transient analysis at high frequencies. Considering that real-world linear sinusoidal AC circuits inherently possess distributed radiation capacitance and inductance, the paper further reveals that, under low- and medium-frequency sinusoidal AC signals, these distributed effects are minimal. Therefore, Kirchhoff’s voltage law and current law can be reliably used as approximate formulas for both transient and steady-state analysis in such frequency ranges. Under high-frequency sinusoidal AC signals, the circuit’s distributed radiation capacitance and inductance become significant and cannot be neglected. As a result, Kirchhoff’s voltage law and current law are no longer valid for transient and steady-state circuit analysis.