Principle: Voltage drop is the reduction in voltage along a conductor due to its resistance (and reactance) when current flows. Every cable has an impedance per unit length, so a current I causes a drop Vdrop = I × Zline over that length. Excessive voltage drop can cause equipment to receive lower voltage than intended, leading to poor performance (e.g. dim lights, motor torque reduction). Therefore, design standards set maximum allowable voltage drop percentages from the source to the load to ensure proper function. In DC or single-phase circuits, Vdrop = I Rtotal. In AC circuits, the impedance Z = √(R² + X²) (with X being inductive reactance) should be considered, and the drop is a complex number (with real and imaginary parts causing phase angle shift), but designers often calculate the magnitude of drop and compare with limits.
Formulas: A practical formula for line voltage drop in cables (from BS 7671 Appendix 4) uses the cable’s tabulated millivolt drop per ampere-meter value. For a given circuit with design current Ib and length L, the drop is calculated using the appropriate mV/A/m from cable tables. For example, if a 10 mm² copper cable has 4.4 mV/A/m and carries 26 A over 20 m, the drop is 4.4 × 26 × 20 / 1000 = 2.29 V. This formula accounts for both resistance and minor reactance in a single coefficient for typical AC frequencies (50/60 Hz).
Alternatively, using fundamental Ohm’s law: if a cable’s resistance is R ohms and reactance is X ohms, then Vdrop = I (R cosφ + X sinφ) for the resistive component of drop (or calculated vectorially for magnitude). For most low-voltage wiring, the simplified approach with tabulated mV/A/m is both accurate and convenient.
Standards and Allowable Limits: Different standards cap the percentage voltage drop from source to load:
Designers calculate drop for each feeder and branch, then select conductors that are sufficiently large or adjust the length to meet these limits. If a run has too much drop, solutions include using a larger cable size (with lower resistance) or adding additional feed points.
A 230 V, 20 A single-phase water heater is 30 m away from the distribution board. Suppose a cable with a resistance of 0.9 Ω per 1000 m (0.0009 Ω/m) is selected. The total loop (out and back) length is 60 m (assuming a single-phase two-wire circuit). The total resistance is calculated as:
R = 0.0009 × 60 = 0.054 Ω
Then the voltage drop is:
Vdrop = I × R = 20 × 0.054 = 1.08 V, which is approximately 1.08 / 230 ≈ 0.47% of the supply voltage. This easily meets a 5% limit. If the run were instead 150 m with the same cable, then R = 0.0009 × 300 = 0.27 Ω and the drop would be 20 × 0.27 = 5.4 V (about 2.35%). While still under 5%, if it were a lighting circuit (with only 3% allowed), the cable might need upsizing or a higher supply voltage if available.
In long-distance transmission, voltage drop (often called line drop) is significant – engineers use higher voltages to mitigate the percentage drop for a given absolute drop (since % = ΔV/V). In DC circuits such as telecom or solar farms, the allowed drop might be only 1–2% to avoid energy waste and ensure proper equipment regulation. For LED lighting, even small voltage drops can affect brightness due to low operating voltage, so designers may run a 24 V LED strip in shorter segments or feed from both ends. In applications like ships and aircraft (often using 115 V or 28 V DC systems), very careful calculations are required due to long cable runs, and specialized standards (e.g., MIL-STD) apply. Although harmonics can slightly increase effective resistance (through the skin effect), for most low-voltage cables this is a minor concern.
Ensuring proper voltage at equipment is critical. A motor at the end of a long line might fail to start if the voltage drop is too high under inrush current conditions. Utilities specify maximum voltage drops in service lines (often around 5% including the distribution network), and construction specifications typically include clauses for maximum voltage drop. Non-compliance can lead to issues such as flickering lights or underperforming HVAC units. Moreover, voltage drop contributes to energy inefficiency due to I²R losses in cables; thus, minimizing drop not only ensures proper voltage delivery but also reduces energy waste. In large facilities, balancing voltage drop and conductor cost is an important economic decision, as larger cables reduce drop but come at higher cost. Modern energy management standards often aim to reduce distribution losses as a means of improving overall efficiency.
Voltage drop calculations can be performed using:
In summary, voltage drop calculation is an essential task in electrical design. It is enforced by standards and facilitated by tables and software, ensuring that all connected equipment receive voltage within their rated range.