Voltage Drop Formula & Example Calculation

What is Voltage Drop?

Voltage drop is the decrease in electrical potential along a current’s path inside an electrical circuit, simply put a “drop in voltage“. It occurs because internal resistance in components such as the power source, passive elements, conductors and connectors dissipates part of the supplied energy.

Voltage drop across an electrical load governs how much supplied power becomes useful energy there. Calculate this drop with Ohm’s law, which ties it to resistance and current.

Voltage Drop in Direct Current Circuits

In direct current circuits, resistance alone causes the drop. Consider a DC circuit with a source and two series-connected resistors, each adding its share to the total voltage drop.

Each element has a specific resistance that determines how much energy it receives and loses. Measuring the voltage at the first resistor shows a value below the supply voltage, because the connecting wire has consumed part of it.

Measuring the voltage across each resistor gives the energy that resistance consumes. As the current flows from the DC supply through the wire toward the first resistor, the conductor resistance already dissipates some of the source energy.

To verify the voltage drop, apply Ohm’s law and Kirchhoff’s circuit law, summarised below.
Ohm’s law states

V → Voltage Drop (V)
R → Electrical Resistance (Ω)
I → Electrical Current (A)

For DC closed circuits, Kirchhoff’s circuit law also serves the voltage drop calculation:
Supply Voltage = Sum of the voltage drops across every component of the circuit.

Voltage Drop Calculation of a DC Power Line

Take a 100 ft power line as an example, so two conductors give 2 × 100 ft. Let the electrical resistance be 1.02Ω/1000 ft and the current be 10 A.

Voltage Drop in Alternating Current Circuits

In AC circuits, Resistance (R) is joined by a second opposition to the flow of current: Reactance (X), which comprises X_C and X_L. Resistance and reactance together form the Impedance (Z).
X_C → Capacitive reactance
X_L → Inductive reactance

The value of Z depends on factors such as magnetic permeability, insulation and the AC frequency.
Mirroring Ohm’s law for DC circuits, the AC form reads

E → Voltage Drop (V)
Z → Electrical Impedance (Ω)
I → Electrical Current (A)

I_B → Full load current (A)
R → Resistance of the cable conductor (Ω/1000ft)
L → Length of the cable (one side) (Kft)
X → Inductive Reactance (Ω/1000f)
V_n → Phase to neutral voltage
U_n → Phase to phase voltage
Φ → Phase angle of the load

Circular Mils and Voltage Drop Calculation

A circular mil is a unit of area describing the circular cross-section of a wire or conductor. The voltage drop in circular mils is given by

L → Wire length (ft)
K → Specific Resistivity (Ω-circular mils/foot)
P → Phase constant (2 for single-phase, 1.732 for three-phase)
I → Electrical current (A), with A denoting the wire’s cross-sectional area in circular mils

Voltage Drop Calculation of Copper Conductor from Table

The voltage drop of a copper wire (conductor) follows from

where f is the factor taken from the standard table below.