In the context of alternating current (AC) electrical systems, the term "instantaneous value" refers to the value of an AC quantity (such as voltage or current) at a specific point in time during its oscillating cycle. AC quantities vary sinusoidally over time, alternating between positive and negative values.
The instantaneous value of an AC voltage or current can be represented as a mathematical function of time, typically described by a sine or cosine waveform. For a sinusoidal AC voltage or current, the instantaneous value can be expressed as:
(
)
=
max
β
sin
β‘
(
2
+
)
i(t)=I
max
β
β
sin(2Οft+Ο)
Where:
(
)
i(t) is the instantaneous current at time
t.
max
I
max
β
is the maximum amplitude (peak value) of the current.
f is the frequency of the AC signal in hertz (Hz).
t is the time variable.
Ο is the phase angle, which represents the shift of the waveform horizontally (time-wise).
Similarly, for AC voltage, the expression would be similar:
(
)
=
max
β
sin
β‘
(
2
+
)
v(t)=V
max
β
β
sin(2Οft+Ο)
Where:
(
)
v(t) is the instantaneous voltage at time
t.
max
V
max
β
is the maximum amplitude (peak value) of the voltage.
f,
t, and
Ο have the same meanings as before.
The instantaneous value of an AC quantity is constantly changing as time progresses, and it traces out a sinusoidal waveform over time. The peak value (
max
I
max
β
or
max
V
max
β
) represents the highest positive or negative point on the waveform, while the phase angle (
Ο) determines the horizontal shift of the waveform.
In AC analysis, understanding instantaneous values is crucial for calculating various parameters such as average values, root mean square (RMS) values, power calculations, and phase relationships between different AC quantities.