Power Formulas in DC and AC Single-Phase & Three-Phase Circuits

Electric Power Formulas & Equations in DC and AC 1-Φ & 3-Φ Circuits

Back to basic, below are the simple Electric Power formulas for Single Phase AC Circuit, Three Phase AC Circuits and DC Circuits. You can easily find electric power in watts by using the following electric power formulas in electric circuits.

Basic Electric Power Formula in AC & DC Circuits

Power Formulas in DC Circuits

• P = V x I
• P = I² x R
• P = V² / R

Power Formulas in Single Phase AC Circuits

• P = V x I x Cos Ф
• P = I² x R x Cos Ф
• P = V² / R (Cos Ф)

Power Formulas in Three Phase AC Circuits

• P = √3 x V_L x I_L x Cos Ф
• P = 3 x V_Ph x I_Ph x Cos Ф
• P = 3 x I² x R x Cos Ф
• P = 3 (V² / R) x Cos Ф

Where:

• P = Power in Watts
• V = Voltage in Volts
• I = Current in Amperes
• R = Resistance in Ohms (Ω)
• Cos Ф = Power Factor

AC Power Formulas in Complex Circuits:

Complex Power & Apparent Power:

When there is an inductor or capacitor in a circuit, the power becomes complex power “S”, meaning it has two parts i.e. real & imaginary part. The magnitude of Complex power is called Apparent power |S|.

Where

• P is the real power
• Q is the reactive power

Active or Real Power & Reactive Power:

The real part is Complex power “S” is known as active or real power “P” & the imaginary part is known as reactive power “Q”.

• S = P + jQ
• P = V I cosθ
• Q = V I sinθ

Where

θ is the phase angle between voltage & current.

Power Factor:

Power factor “PF” is the ratio of real power “P” to apparent power “|S|”. Mathematically, Power factor is the cosine of angle θ between real power and apparent power.

Where

|S| = √(P²+Q²)

Other formulas used for Power Factor are as follow:

Cosθ = R/Z

Where:

• Cosθ = Power Factor
• R = Resistance
• Z = Impedance (Resistance in AC circuits i.e. X_L, X_C and R known as Inductive reactance, capacitive reactance and resistance respectively).

Cosθ = kW / kVA

Where

• Cosθ = Power Factor
• kW = Real Power in Watts
• kVA = Apparent Power in Volt-Amperes or Watts

Additional formulas used for power factor.

• Cosθ = P / V I
• Cosθ = kW / kVA
• Cosθ = True Power/ Apparent Power

Real Power Of Single Phase & 3-Phase Current

Where

• V_rms  & I_rms is the root mean square value of voltage & current respectively.
• V_L-N  & I_L-N  is the line-to-neutral voltage & current respectively.
•  V_L-L & I_L-L  is the line-to-line voltage & current respectively.
• Cosθ is the power factor PF.

Reactive Power Of Single & 3-Phase Current:

Where

θ = is the phase angle i.e. phase difference between voltage and current.

The following table shows the different electrical power formulas in both AC and DC circuits.

Quantity	DC	AC (1-Phase)	AC (3-Phase)
Power (W)	P = V x I P = I2 x R P = V2 / R	P = V x I x Cos Ф P = I2 x R x Cos Ф P = V2 / R (Cos Ф)	P = √3 x VL x IL x Cos Ф P = 3 x VPh x IPh x Cos Ф P = 3 x I2 x R x Cos Ф P = 3 (V2 / R) x Cos Ф

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