Enter the maximum voltage (volts), the maximum current (amps), voltage phase angle, current phase angle, time, and the angular frequency (rad/s) into the calculator to determine 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 (amps)
  • 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) = 398.405 (amps)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

maximum voltage (volts) = 15

maximum current (amps) = 412

angular frequency (rad/s) = 2

time (s) = 15

phase angles (rad) = 14 & 5

Enter these given values into the calculator or above yields: 

P(t) = 15*412*cos(2*15+14)*cos(2*15+5) = -5583.94 (amps)