In an alternating-current (AC) system, voltages and currents vary with time and commonly reverse sign periodically. A sinusoidal voltage can be written

$$v(t)=V_m\cos(\omega t+\phi_v),$$

and a sinusoidal current as

$$i(t)=I_m\cos(\omega t+\phi_i).$$

Sign means direction or polarity

A negative current does not mean a negative amount of charge. It means the actual current direction is opposite to the chosen positive reference direction.

Likewise, a negative voltage means the instantaneous polarity is opposite to the chosen voltage reference.

Amplitude and frequency

$V_m$ and $I_m$ are peak magnitudes. The angular frequency $\omega$ determines how quickly the quantities repeat:

$$\omega=2\pi f.$$

Voltage and current in one steady-frequency AC system normally share the same frequency even when their peaks occur at different times.

Phase difference

The difference

$$\phi_v-\phi_i$$

describes how voltage and current are shifted relative to one another.

A positive phase difference means the voltage waveform reaches corresponding points in its cycle earlier than the current; a negative value means it lags behind.

Resistors, capacitors and inductors produce different phase relationships between voltage and current.

Sinusoidal AC can be understood directly in the time domain. For more advanced steady-state circuit calculations, the same sinusoids can later be represented by phasors and manipulated using complex algebra.