A <lagging power factor> describes an absorbing sinusoidal <electrical load> whose <electric current> lags its terminal <electric potential difference>. With the <passive sign convention>, choose
$$
v(t)=\sqrt2V\cos\omega t,\qquad i(t)=\sqrt2I\cos(\omega t-\varphi),\qquad 0<\varphi\le\pi/2.
$$
The current maximum occurs later by $\varphi/\omega$. The <RMS phasors> give <complex electrical power>
$$
S=VI^*=VI(\cos\varphi+i\sin\varphi),\qquad
P=VI\cos\varphi,\quad Q=VI\sin\varphi>0.
$$
In this equation the supply phasor is the real number $V$, while $I^*$ denotes the conjugate of the current phasor. Positive $Q$ is inductive <reactive power> under this convention. The primary MIT notes derive the conjugation and the peak-versus-RMS factor.<AC Power Flow in Linear Networks by James L. Kirtley Jr.>[Energy and Power, equations 61–65; §7.1]{ref}

For an original $230\,\mathrm V$, $10\,\mathrm A$ example with $\cos\varphi=0.8$, <active power> is $1840\,\mathrm W$ and <reactive power> is $1380\,\mathrm{var}$. At $50\,\mathrm{Hz}$, $\varphi\approx0.6435$ radians corresponds to a current delay of about $2.05\,\mathrm{ms}$. The factor $0.8$ gives the magnitude of the phase relationship, while the word lagging supplies the direction lost by the cosine.

An ideal <inductor> is the limiting case $\varphi=\pi/2$: it alternately stores and returns magnetic <energy>, with zero mean <active power>. An absorbing resistive-inductive load usually has both positive <active power> and positive <reactive power>. An ideal parallel <capacitor> can reduce the source's quadrature <electric current>; sufficient extra <capacitance> eventually crosses into <leading power factor> rather than improving the factor indefinitely.

For distorted waveforms, specify whether lagging refers to the fundamental <displacement power factor>; one phase angle does not characterize arbitrary <harmonic components>. A signed meter display is also not a universal lead/lag label. The manufacturer's sign-convention explanation distinguishes phase direction from the convention used for displayed factor signs.<Power factor sign conventions in Schneider Electric FAQ FA212521>[Resolution, lead/lag description and IEC/IEEE display-convention diagrams]{ref}


 Lagging power factor (source code)