 Basic Voltage, Current, Power and Resistance Formulas in AC and DC Circuits Following are the electrical engineering formulas and equations for the basic quantities i.e. currentvoltagepowerresistance and impedance in both DC and AC circuits (single-phase and three-phase).

Electrical Current Formulas

Electrical Current Formulas in DC Circuit

• I = V/R
• I = P/V
• I = √P/R

Electrical Current Formulas in Single Phase AC Circuit

• I = P / (V x Cosθ)
• I = (V/Z)

Electrical Current Formulas in Three-Phase AC Circuit

• I = P / √3 x V x Cosθ

The voltage or Electrical Potential Formulas

Electrical Potential or Voltage Formula in DC Circuits

• V = I x R
• V = P / I
• V = √ (P x R)

The voltage or Electrical Potential Formulas in Single Phase AC Circuits

• V = P/(I x Cosθ)
• V = I x Z

Voltage Formulas in Three-Phase AC Circuits

• VL = √3 VPH or VL = √3 EPH     …     [Star Connection]
• VL = VPH     …     [Delta Connection]

Electric Power Formulas

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 Cosθ
• P = I2 x R Cosθ
• P = (V2/R) Cosθ

Power Formulas in Three-Phase AC Circuits

• P = √3 x VL x IL Cosθ
• P = 3 x VP x IP Cosθ

Electrical Resistance Formulas

Electrical Resistance and Impedance Formulas in DC Circuits

• R = V/I
• R = P/I2
• R = V2/P

Electrical Resistance and Impedance Formulas in AC Circuits

In AC Circuits (capacitive or inductive load), Resistance = Impedance i.e., R = Z

• Z2 = R2 + X2 … In case of resistance and reactance
• Z = √(R2 + XL2) … In case of Inductive load
• Z = √(R2 + XC2) … In case of Capacitive load
• Z = √(R2 + (XL– XC)2… In the case of both inductive and capacitive loads.

Impedance is the resistance of AC circuits i.e. resistive, captative and inductive circuit (already mentioned above). Where “Z” is the impedance in ohms, “R” is resistance in Ohms and “X” is the reactances in Ohms.

Good to know

• I = Current in Amperes (A)
• V = Voltage in Volts (V)
• P = Power in Watts (W)
• R = Resistance in Ohm (Ω)
• Z = impedance = Resistance of AC Circuits in Ohms
• Cosθ = Power factor = Phase difference between voltage and current in AC circuits
• VPH = Phase Voltage
• VL = Line Voltage

Also

X= Inductive reactance

X= 2πfL…Where L = Inductance in Henry

And

XC = Capacitive reactance

XC = 1/2πfC… Where C = Capacitance in Farads.

Also, ω = 2πf

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The following table shows the current, voltage, power and resistance equations and formulas in DC and 1-Φ and 3-Φ AC circuits.

 Quantity DC Single Phase AC Three Phase AC Current(I) I = V/RI = P/VI = √P/R I = P / (V x Cosθ)I = (V/Z) I = P / √3 x V x Cosθ Voltage(V) V = I x RV = P / IV = √ (P x R) V = P/(I x Cosθ)V = I / Z VL = √3 VPH or VL = √3 EPHVL = VPH Power(P) P = IVP = I2RP = V2/R P = V x I x CosθP = I2 x R x CosθP = (V2/R) x Cosθ P = √3 VL IL CosФP = 3 VPh IPh CosФ Resistance(R) R = V/IR = P/I2R = V2/P Z = √(R2 + XL2)Z = √(R2 + XC2)Z = √(R2 + (XL– XC)2

Conductance

G = 1 / R

It is the reciprocal (i.e. inverse) of resistance. The unit of conductance is Siemen or Mho and represented by the symbol of “G” or “℧”.

Capacitance

C = Q / V

Where “C” is the capacitance in farads,  “Q” is charge in coulombs, and “V” is the voltage in volts. The unit of capacitance is Farad “F” or microfarad “μF”.

Inductance

VL = -L (di / dt)

Where “L” is the inductance in Henrys, “VL” is the instantaneous voltage across the inductor in volts and “di/dt” is the rate of changes in current in Amperes per second. The unit of Inductance “L” is Henrys “H”. It is also known as Ohm’s law for inductance.

Charge

Q = C x V

Where “Q” is the charge in coulombs, “C” is the capacitance in farads and “V” is the voltage in Volts.

Frequency

f = 1 / T

Time Period

T = 1 / f

Where “f” is the frequency in Hertz (Hz) and “T” is the time periods in seconds.