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If you probe an AC wall socket with an oscilloscope, the voltage never sits still β€” it continuously surges positive, collapses to zero, and reverses polarity hundreds of times every second.
Because alternating signals change constantly over time, engineers need three distinct descriptors to describe their size: instantaneous, peak, and peak-to-peak voltage.
How do we pinpoint the exact voltage at any fractional microsecond along that curve?

Instantaneous Voltage

Instantaneous voltage, denoted by lowercase vv or v(t)v(t), is the value of an alternating voltage at one specific, isolated instant in time.
For a pure sine wave with zero initial phase offset, this instantaneous value follows the mathematical relation v(t)=V0sin⁑(Ο‰t)v(t) = V_0 \sin(\omega t), where Ο‰\omega represents the angular frequency (the rate of cycle rotation in radians per second).
While v(t)v(t) constantly varies, what defines the outer physical boundaries of this continuous swing?

Peak and Peak-to-Peak Values

Peak voltage (V0V_0 or VpV_p) is the maximum displacement of the waveform from its center zero-volt reference line, representing the wave's amplitude.
Peak-to-peak voltage (VppV_{pp}) is the total vertical potential difference between the maximum positive crest (+V0+V_0) and the minimum negative trough (βˆ’V0-V_0).
Because a standard sinusoidal wave is symmetrical about the 0Β V0\text{ V} axis, the crest sits at +V0+V_0 and the trough sits at βˆ’V0-V_0, leading to the fundamental relation Vpp=V0βˆ’(βˆ’V0)=2V0V_{pp} = V_0 - (-V_0) = 2V_0.