Instantaneous Power Calculator

Formula

The formula to calculate the Instantaneous Power (P(t)) is:

\[ P(t) = V_m \cdot I_m \cdot \cos(\omega t + a_v) \cdot \cos(\omega t + a_i) \]

Where:

\(P(t)\) is the Instantaneous Power (watts)
\(V_m\) is the maximum voltage (volts)
\(I_m\) is the maximum current (amps)
\(\omega\) is the angular frequency (rad/s)
\(t\) is the time (s)
\(a_v\) is the voltage phase angle (rad)
\(a_i\) is the current phase angle (rad)

What is Instantaneous Power?

Instantaneous power is the power at any given moment in time in an AC circuit. It varies with time and is calculated using the product of the instantaneous voltage and current values. This calculation helps in understanding the dynamic behavior of power in AC circuits, which is essential for designing and analyzing electrical systems.

Example Calculation

Let's assume the following values:

Maximum Voltage (Vm) = 10 volts
Maximum Current (Im) = 5 amps
Angular Frequency (w) = 2 rad/s
Time (t) = 1 second
Voltage Phase Angle (av) = 0.5 rad
Current Phase Angle (ai) = 0.3 rad

Using the formula:

\[ P(t) = 10 \cdot 5 \cdot \cos(2 \cdot 1 + 0.5) \cdot \cos(2 \cdot 1 + 0.3) \] \[ P(t) = 50 \cdot \cos(2.5) \cdot \cos(2.3) \approx 50 \cdot (-0.801) \cdot (-0.666) \approx 26.69 \]

The Instantaneous Power (P(t)) is approximately 26.69 watts.