Voltage is the electrical potential difference between two points, often described as the “pressure” that drives electric current through a circuit. In any real-world electrical system, voltage drop occurs, representing a loss of this electrical potential along the conductor’s path. This decrease in voltage happens because all conductors possess some degree of opposition to current flow. Calculating this drop is necessary for designing safe and efficient electrical systems, ensuring equipment receives the correct operating voltage and preventing poor performance or damage.
The Physics Behind Voltage Drop
The underlying reason for voltage drop is the inherent resistance found in all electrical conductors. Resistance is the opposition a material offers to the passage of electric current, converting some electrical energy into heat. As current flows through the wire’s resistance, a portion of the voltage is consumed, resulting in the drop.
This relationship is governed by Ohm’s Law, which states that the voltage across a conductor is directly proportional to the current flowing through it. Mathematically, this is expressed as \(V = I \times R\), where \(V\) is the voltage, \(I\) is the current in amperes, and \(R\) is the resistance in ohms. In the context of the wire, the conductor acts as a resistor, and the voltage drop is the potential difference measured across its length. The greater the current or the greater the conductor’s resistance, the larger the resulting voltage drop will be.
Applying Ohm’s Law to Calculate Voltage Drop
The simplest theoretical formula for voltage drop directly applies Ohm’s Law to the conductor: \(V_d = I \times R\). Here, \(V_d\) is the voltage drop in volts, \(I\) is the total current in amperes, and \(R\) is the total resistance of the conductor path in ohms. This calculation is straightforward when the total resistance of the wire is a known value.
For example, if a complete circuit path (supply and return wires) has a total resistance of \(0.5\ \Omega\) and a current of \(20\ \text{A}\) flows through it, the voltage drop would be \(20\ \text{A} \times 0.5\ \Omega\), resulting in a \(10\ \text{V}\) loss. This method provides a quick way to assess the loss once the total conductor resistance has been determined.
While this formula provides the theoretical basis, in most real-world applications, the resistance value \(R\) is not a fixed component and must be derived from the wire’s physical properties, leading to more comprehensive formulas.
Practical Formulas Based on Wire Properties
In real-world electrical design, the resistance of the wire is rarely a given value. It must be calculated using a formula that accounts for the conductor’s physical characteristics. Resistance is directly proportional to the wire’s length and material resistivity, and inversely proportional to its cross-sectional area. This means longer wires and smaller-gauge wires have higher resistance, leading to a greater voltage drop.
The full practical formula for calculating voltage drop in a direct current (DC) circuit is:
$\(V_d = \frac{2 \times K \times I \times L}{CM}\)$
In this formula, \(V_d\) is the voltage drop in volts, \(I\) is the current in amperes, and \(L\) is the one-way length of the conductor in feet. \(CM\) represents the cross-sectional area of the wire in circular mils, which is a standard unit for wire gauge.
The constant \(K\) is the specific resistivity of the conductor material, often referred to as the K-factor, measured in \(\text{Ohm} \cdot \text{circular mil}/\text{foot}\) at a standard temperature. For copper, \(K\) is typically \(12.9\), and for aluminum, it is approximately \(21.2\). The multiplier of 2 accounts for the total length of the circuit, including both the supply and return wires.
For single-phase alternating current (AC) circuits, the same core formula applies. For larger AC conductors, the calculation becomes more complex due to the effects of inductance and skin effect, requiring the use of impedance (\(Z\)) instead of resistance (\(R\)). The formula may also incorporate a power factor correction, which accounts for the phase difference between voltage and current in an AC system, though the basic resistive formula is sufficient for smaller wires.
Consequences and Acceptable Voltage Drop Limits
Excessive voltage drop negatively impacts the performance and longevity of connected electrical equipment. When the voltage delivered to a load is lower than its design voltage, resistive loads like heating elements or incandescent lights will not provide their rated output, resulting in diminished performance.
For inductive equipment, such as motors, low operating voltage causes the motor to draw more current to compensate for lost power, leading to overheating and premature failure. Additionally, the heat generated by the voltage drop in the conductors represents wasted energy and can pose a safety hazard if the wire insulation overheats.
To ensure reasonable efficiency and proper operation, industry standards provide guidelines for maximum allowable voltage drop. The National Electrical Code (NEC) provides informational notes recommending that the voltage drop on branch circuits should not exceed 3% of the supply voltage. Furthermore, the maximum total voltage drop, including both the feeder and the branch circuit, should be limited to 5% from the service point to the farthest outlet.
For example, on a \(120\ \text{V}\) branch circuit, a 3% drop is \(3.6\ \text{V}\), meaning the voltage delivered to the load should be no less than \(116.4\ \text{V}\). While these are recommendations and not mandatory rules in all jurisdictions, adhering to these limits is standard practice for designing robust and energy-efficient electrical installations.