Voltage Drop Formula & Example Calculation

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Key learnings:
  • Voltage Drop Definition: Voltage drop is the reduction in electrical potential along a circuit’s path, mainly due to resistance and reactance in the components.
  • Calculation Formula: The voltage drop calculation formula involves Ohm’s law, which uses resistance, current, and impedance values to determine the decrease in voltage.
  • DC Circuits Example: In DC circuits, voltage drop is directly proportional to the resistance and current, illustrated by a series resistor example.
  • AC Circuits Complexity: AC voltage drop calculations include impedance, which combines both the resistive and reactive properties of the circuit.
  • Circular Mils Usage: Circular mils measure the wire’s cross-sectional area, which is crucial for accurate voltage drop calculation in electrical installations.

What is Voltage Drop?

Voltage drop is defined as the decrease in electrical potential along a current’s path within an electrical circuit—simply put, a “drop in voltage.” It occurs due to internal resistance in various components like the power source, passive elements, conductors, and connectors, leading to undesirable energy loss.

Voltage drop across an electrical load directly relates to the power that can be transformed into useful energy. This drop is calculated using Ohm’s law, which ties it to resistance and current.

Voltage Drop in Direct Current Circuits

In direct current circuits, resistance causes voltage drop. To illustrate, consider a DC circuit example with a source and two series-connected resistors, each contributing to the total voltage drop.

Each element in the circuit has a specific resistance that affects how much energy it receives and loses. Measuring the voltage across the DC supply and the first resistor shows it’s less than the supply voltage due to these resistances.

We can calculate the energy consumed by each resistance by measuring the voltage across individual resistors. While the current flows through the wire starting from the DC supply to the first resistor, some energy given by the source gets dissipated due to the conductor resistance.

To verify the voltage drop, Ohm’s law and Kirchhoff’s circuit law are used, which are briefed below.
Ohm’s law is represented by

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

For DC closed circuits, we also use Kirchhoff’s circuit law for voltage drop calculation. It is as follows:
Supply Voltage = Sum of the voltage drop across each component of the circuit.

Voltage Drop Calculation of a DC Power Line

Here, we are taking an example of a 100 ft power line. So, for 2 lines, 2 × 100 ft. Let Electrical resistance be 1.02Ω/1000 ft, and current be 10 A.

Voltage Drop in Alternating Current Circuits

In AC circuits, in addition to Resistance (R), there will be a second opposition for the flow of currentReactance (X), which comprises XC and XL. Both X and R will oppose the current flow also. The sum of the two is termed Impedance (Z).
XC → Capacitive reactance
XL → Inductive reactance

The amount of Z depends on the factors such as magnetic permeability, electrical isolating elements, and AC frequency.
Similar to Ohm’s law in DC circuits, here it is given as

E → Voltage Drop (V)
Z → Electrical Impedance (Ω)
I → Electrical Current (A)
voltage drop in alternating current circuits
IB → 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)
Vn → Phase to neutral voltage
Un → Phase to phase voltage
Φ → Phase angle of the load

Circular Mils and Voltage Drop Calculation

A circular mil is really a unit of area. It is used for referring to the circular cross-sectional area of the wire or conductor. The voltage drop using mils is given by

L → Wire length (ft)
K → Specific Resistivity (Ω-circular mils/foot).
P → Phase constant = 2 meant for single-phase = 1.732 meant for three-phase
I → Area of the wire (circular mils)

Voltage Drop Calculation of Copper Conductor from Table

The voltage drop of the copper wire (conductor) can be found out as follows:

f is the factor we get from the standard table below.

SIZE OF COPPER CONDUCTORFACTOR, f
AWGmm2SINGLE-PHASETHREE-PHASE
142.080.4760.42
123.310.3130.26
105.260.1960.17
88.370.1250.11
613.30.08330.071
421.20.05380.046
3 0.04310.038
233.60.03230.028
142.40.03230.028
1/053.50.02690.023
2/067.40.02220.020
3/085.00.0190.016
4/0107.20.01610.014
250 0.01470.013
300 0.01310.011
350 0.01210.011
400 0.01150.009
500 0.01010.009
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