Enter the peak (maximum) voltage (volts), the peak (maximum) current (amps), voltage phase angle, current phase angle, time, and the angular frequency (rad/s) into the calculator to determine the instantaneous power for sinusoidal AC waveforms.

Instantaneous Power Calculator

Enter all fields to calculate the Instantaneous Power.

Instantaneous Power Formula

The following formula is used to calculate the Instantaneous Power.

P(t) = Vm*Im*cos(wt+av)*cos(wt+ai)
  • Where P(t) is the instantaneous power (watts)
  • Vm is the maximum voltage (volts) 
  • Im is the maximum current (amps) 
  • w is the angular frequency (rad/s) 
  • t is the time (s)
  • av is the voltage phase angle (rad)
  • ai is the current phase angle (rad)

How to Calculate Instantaneous Power?

The following example problems outline how to calculate Instantaneous Power.

Example Problem #1

  1. First, determine the maximum voltage (volts). In this example, the maximum voltage (volts) is determined to be 15.
  2. Next, determine the maximum current (amps). For this problem, the maximum current (amps) is 40.
  3. Next, determine the angular frequency (rad/s). In this case, the angular frequency (rad/s) is found to be 12.
  4. Next, determine the time. For this problem, the time is 5 seconds.
  5. Next, determine the voltage and current phase angle. These are 2 and 3 rad, respectively.
  6. Finally, calculate the Instantaneous Power using the formula above: 

P(t) = Vm*Im*cos(wt+av)*cos(wt+ai)

Inserting the values from above and solving yields: 

P(t) = 15*40*cos(12*5+2)*cos(12*5+3) = 95.4011 (watts)

FAQ

What is Instantaneous Power in electrical circuits?

Instantaneous power is the power at a specific moment in time in an electrical circuit, and in general it is defined as p(t) = v(t) × i(t). For sinusoidal AC waveforms (using peak values and phase angles), it can be calculated using the maximum voltage, maximum current, angular frequency, time, and the phase angles of voltage and current. It varies over time, especially in AC (Alternating Current) circuits.

How does the phase angle affect Instantaneous Power?

The phase angle, both for voltage (av) and current (ai), indicates the shift in phase between the voltage and current waveforms. This affects the cosine terms in the instantaneous power formula, thereby influencing the power value. In AC circuits, the phase difference is also crucial for calculating the real (average) power consumed.

Why is calculating Instantaneous Power important?

Calculating instantaneous power is essential for understanding the performance of electrical systems, especially in AC circuits where power varies over time. It helps in analyzing power flow, designing electrical systems, and ensuring the safe operation of electrical devices by not exceeding their power ratings.