Voltage Drop and Power Formulas for Electrical Engineers

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Working with single phase, three-phase and DC (direct current circuits) and you quickly need to reference formulas for voltage drops and power calculations for a given conductor? The table below provides a quick reference for these calculations.

Voltage Drop and Power Calculation Formulas For Single Phase Circuits

Electrical Parameters	Formulas
Voltage Drop	$∆V = 2*I*L*(rCosՓ + xSinՓ)$
% Voltage Drop	% $∆V  =  \frac{∆V}{V_r}*100$
Active Power	$P = V*I*CosՓ$
Reactive Power	$Q = V*I*SinՓ$
Apparent Power	$S =  V*I = \sqrt{{P^2} +{Q^2}}$
Power Factor	$CosՓ = \frac{P}{S}$
Power Loss	$P_L = 2*L*r*I^2$

Voltage Drop and Power Calculation Formulas For Three-Phase Circuits

Electrical Parameters	Formulas
Voltage Drop	$∆V = \sqrt{3}*I*L*(rCosՓ + xSinՓ)$
% Voltage Drop	% $∆V = \frac{∆V}{V_r}*100$
Active Power	$P = \sqrt{3}*V*I*CosՓ$
Reactive Power	$Q = \sqrt{3}*V*I*SinՓ$
Apparent Power	$S = \sqrt{3}*V*I = \sqrt{{P^2} +{Q^2}}$
Power Factor	$CosՓ = \frac{P}{S}$
Power Loss	$P_L = 3*L*r*I^2$

Voltage Drop and Power Calculation Formulas For Direct Current (DC) Circuits

Electrical Parameters	Formulas
Voltage Drop	$∆V = 2*I*L*r$
% Voltage Drop	% $∆V = \frac{∆V}{V_r}*100$
Active Power	$P = V*I$
Reactive Power	$-$
Apparent Power	$-$
Power Factor	$-$
Power Loss	$P_L = 2*L*r*I^2$

Meaning of symbols used in the formulas above:
$L$       =   Total length of conductor
$r$       =    Resistance of conductor per unit length
$x$       =    Reactance of conductor per unit length
$∆V$    =   Voltage drop 
$P$       =   Active power
$Q$      =    Reactive power
$I$        =   Current