Basic Electrical Engineering Formulas and Equations

Electrical Technology

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. current, voltage, power, resistance and impedance in both DC and AC circuits (single phase and three phase).

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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

Voltage or Electrical Potential Formulas

Electrical Potential or Voltage Formula in DC Circuits

V = I x R
V = P / I
V = √ (P x R)

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

V_L = √3 V_PH or V_L = √3 E_PH … [Star Connection]
V_L = V_PH … [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 V_L x I_L Cosθ
P = 3 x V_P x I_P Cosθ

Electrical Resistance Formulas

Electrical Resistance & Impedance Formulas in DC Circuits

R = V/I
R = P/I²
R = V²/P

Electrical Resistance & 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 + X_L²) … In case of Inductive load
Z = √(R² + X_C²) … In case of Capacitive load
Z = √(R² + (X_L– X_C)²… In 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
V_PH = Phase Voltage
V_L = Line Voltage

Also,

X_L= Inductive reactance

X_L= 2πfL…Where L = Inductance in Henry

And;

X_C = Capacitive reactance

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

Also, ω = 2πf

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

Quantity	DC	Single Phase AC	Three Phase AC
Current (I)	I = V/R I = P/V I = √P/R	I = P / (V x Cosθ) I = (V/Z)	I = P / √3 x V x Cosθ
Voltage (V)	V = I x R V = P / I V = √ (P x R)	V = P/(I x Cosθ) V = I / Z	V_L = √3 V_PH or V_L = √3 E_PH V_L = V_PH
Power (P)	P = IV P = I²R P = V²/R	P = V x I x Cosθ P = I² x R x Cosθ P = (V²/R) x Cosθ	P = √3 V_L I_L CosФ P = 3 V_Ph I_Ph CosФ
Resistance (R)	R = V/I R = P/I² R = V²/P	Z = √(R² + X_L²) Z = √(R² + X_C²) Z = √(R² + (X_L– X_C)²

Other Additional Electrical Quantities Formulas

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

Inductance:

V_L = -L (di / dt)

Where “L” is inductance in Henrys, “V_L” 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 frequency in Hertz (Hz) and “T” is the time periods in seconds.