Power Formulas in DC and AC 1-Phase and 3-Phase Circuits . Electrical power is a fundamental concept in electrical engineering, determining how energy is transferred and utilized in electrical circuits. Whether in DC or AC circuits, power calculation is essential for designing and analyzing electrical systems efficiently.
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What is Electric Power?
Electrical Energy is one of the widely used forms of energy in our day to day lives whether it is in the form of AC Mains power or batteries. Our utility company supplies this electrical energy in the form of electric potential and current and the rate at which electrical energy transfers in an electrical circuit is known as Electrical Power.
In terms of Physics, Energy is the ability to do Work and the rate of doing that Work is known as Power.
So, if P is the Power, W is the Work and t is the time, then
Power P = Work done in unit time = W/t
The units of power are Watts.
We know that the Electric Potential is the amount of Work done in moving a unit charge and current is the rate of movement of charge.
Using the above statement, we can rewrite the previous power equation as:
P = W/t = (W/Q) × (Q/t) Watts
The first term (W/Q) represents the electric potential (V) while the second term (Q/t) represents the current (I).
So, Electric Power P = V × I.
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Types of Power in Electrical Circuits
Power in electrical circuits is categorized into:
- Real Power (P): The actual power consumed by a device, measured in watts (W).
- Reactive Power (Q): Power stored and released in inductive or capacitive elements, measured in volt-amperes reactive (VAR).
- Apparent Power (S): The total power in a circuit, measured in volt-amperes (VA).
Basic Electric Power Formula in AC and 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)
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Power Formulas in Three Phase AC Circuits
- 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
Where:
- P = Power in Watts
- V = Voltage in Volts
- I = Current in Amperes
- R = Resistance in Ohms (Ω)
- Cos Ф = Power Factor
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AC Power Formulas in Complex Circuits:
Complex Power and 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 and 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
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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. XL, XC and R known as Inductive reactance, capacitive reactance and resistance respectively).
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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 and 3-Phase Current
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Where
- Vrms and Irms is the root mean square value of voltage & current respectively.
- VL-N & IL-N is the line-to-neutral voltage & current respectively.
- VL-L & IL-L is the line-to-line voltage & current respectively.
- Cosθ is the power factor PF.
Reactive Power Of Single and 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) |
|
|
|
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Common Mistakes in Power Calculations
Avoid these common mistakes:
- Ignoring the power factor in AC calculations
- Using incorrect voltage values for star/delta connections
- Confusing real, reactive, and apparent power
FAQs
What is the main difference between DC and AC power formulas?
DC power formulas involve simple calculations without phase angles, while AC power formulas require considering power factor and phase angles.
Why is power factor important in AC circuits?
Power factor affects energy efficiency. A low power factor increases losses and reduces the effective power usage in electrical systems.
What is the difference between real, reactive, and apparent power?
- Real Power (P): Actual power consumed.
- Reactive Power (Q): Power due to inductance/capacitance.
- Apparent Power (S): Combination of real and reactive power.
How can I improve power factor in my system?
Using capacitors or synchronous condensers can improve power factor, reducing losses and improving efficiency.
Why are 3-phase systems more efficient than 1-phase systems?
Three-phase systems deliver more power with less conductor material and improved efficiency, making them ideal for industrial applications.
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