# Voltage drop

A voltage drop or voltage drop is the electrical voltage that arises in a circuit as a result of an electrical current flowing through an electrical component . The term is in contrast to the source voltage , which is not caused by a current, but on the contrary can cause a current.

The term voltage drop is used in the IEV introduced for the standardization of basic technical terms . The term voltage drop is also used in other standards and for the most part in specialist literature.

The physical quantity voltage characterizes a potential difference between two points of an electric field independent of an electric current . This voltage exists even if there is no current at the same moment. In contrast, one speaks of a voltage drop precisely when the energy used to separate unlike charges in a voltage source is released again by the current . According to the consumer arrow system preferred in electrical engineering , voltage drop and current intensity have the same direction.

The voltage drop at the consumer results in an external energy release. In contrast, a source voltage is connected to an energy supply in a circuit with a consumer.

## Voltage drop across resistors

Voltage drops on every passive component when current flows through it. The borderline case of a short circuit is an exception .

Linear resistance

A passive component often behaves like a linear resistor . In many simple cases, its behavior can be roughly described by labeling it as an ohmic resistance . A voltage drops across this in proportion to the current strength , as indicated by Ohm's law . It applies to constant quantities as well as to effective values and instantaneous values of alternating quantities.

On components that have the behavior of an inductance or a capacitance , the relationship between current strength and voltage drop is also dependent on time. In the technically important stationary process of sinusoidal alternating quantities, the relationship can be represented as reactance . The proportionality between current and voltage applies here to the rms values ​​and amplitudes .

Non-linear resistance

Almost all semiconductor components and a number of other passive components can only be described as non-linear resistance . For example, in the case of a diode that is operated in the technically preferred current intensity range, the voltage drop is proportional to the logarithm of the current intensity. Only in the case of small current changes can the relationship with the small voltage changes that then occur can be approximated linearly using a differential resistance . This is obtained from their small signal behavior . In general, the voltage drop across non-linear components can only be described to a limited extent using empirically obtained formulas, characteristics or small-signal equivalent circuit diagrams .

## Voltage drop according to the Kirchhoff rules

The sum of all voltage drops across the lines and consumables is as large as the voltage of the voltage source. In one cycle with partial voltages of an electrical direct current network, the following formula applies: ${\ displaystyle n}$

${\ displaystyle \ sum _ {k = 1} ^ {n} U_ {k} = 0}$

( Mesh rule from the Kirchhoff rules)

In AC networks, complex rms values ​​or complex amplitudes of the voltages must be added to the sum .

## Voltage drop in power engineering

In the field of electrical power engineering , the voltage drop on lines and their connection points should be kept within limits so that the operating voltage of the equipment is sufficiently high and the losses are kept within reasonable limits. A higher voltage drop is permitted when starting motors and for other equipment with high inrush currents, provided that in all cases the voltage fluctuations are within the limits permissible for the equipment.

### Calculation of the voltage drop on electrical lines

Voltage drop on the connecting cables ${\ displaystyle R _ {\ text {outside}}}$

According to DIN VDE 0100–520: 2012–06 Appendix G , the voltage drop in the area of low-voltage networks in electrical lines for practical applications can be calculated as an approximation and neglecting the transverse voltage drop using the following formula:

${\ displaystyle U = L \, b \ left ({\ frac {\ rho} {S}} \ cos \ varphi + X '\ sin \ varphi \ right) I _ {\ text {B}}}$

Are there

• ${\ displaystyle U}$ ... voltage drop
• ${\ displaystyle L}$ ... Straight length of the cable and line system
• ${\ displaystyle b}$ ... coefficient:
${\ displaystyle b = 1}$ for three-phase circuits
${\ displaystyle b = 2}$ for single-phase circuits (forward and return lines)
Note: Three-phase circuits that are loaded completely asymmetrically (only one outer conductor is loaded) behave like single-phase circuits. With the usually symmetrical load (all three outer conductors equally loaded), no conductor current flows in the neutral conductor , so there is no voltage drop there.
• ${\ displaystyle \ rho}$   … Specific electrical resistance of the conductors in undisturbed operation.
The specific electrical resistance is taken as the value for the temperature present in undisturbed operation or 1.25 times the specific electrical resistance at 20 ° C, or 0.0225 Ωmm 2 / m for copper and 0.036 Ωmm 2 / m for aluminum.
• ${\ displaystyle S}$   ... cross section of the ladder
• ${\ displaystyle \ cos \ varphi}$... power factor; if not known, a value of 0.8 is assumed (accordingly )${\ displaystyle \ sin \ varphi = 0 {,} 6}$
• ${\ displaystyle X '}$… Line covering with reactance; if not known, a value of 0.08 mΩ / m is assumed
• ${\ displaystyle I _ {\ text {B}}}$ ... operating current

The relative voltage drop results from:

${\ displaystyle {\ frac {U} {U_ {0}}} = {\ frac {U} {U_ {0}}} \ cdot 1 = {\ frac {U} {U_ {0}}} \ cdot 100 \, \% = {\ frac {100 \, U} {U_ {0}}} \, \%}$

Stands for the respective system voltage. ${\ displaystyle {U_ {0}}}$

Note: In low-voltage circuits, the limit values ​​for the voltage drop must only be complied with for circuits for lights (not e.g. for bell, control, door opener) (provided that the proper function of this equipment is checked).

### Limit values ​​in Germany

 up to 100 k VA 0.5% 100-250 kVA 1.0% 250-400 kVA 1.25% over 400 kVA 1.5%
• According to DIN VDE 0100-520, according to Table G.52.1, the voltage drop in consumer systems between the house connection and consumables (sockets or device connection terminals) should not be more than 3% for lighting systems and 5% for other electrical consumables.
• According to DIN 18015 Part 1, the voltage drop between the meter and the sockets or device connection terminals should not be more than 3%.

The basis is the mains voltage , which is defined as 230/400 V for Europe in accordance with DIN IEC 38, as well as the nominal current strength of the overcurrent protection devices , e.g. 63 A or 16 A.

### Longitudinal and transverse voltage drop

Simplified electrical line with series impedance and vector diagrams with different loads

In the general case, which is based on the complex AC calculation in the description , the voltage difference on a line operated with AC voltage is not identical to the difference in the magnitudes of the voltages between the beginning and the end of the line. In certain cases, the amount of voltage increased along the line. The terms longitudinal and transverse voltage drop are used to describe these voltage differences, especially in electrical power engineering and high voltage engineering.

The sketch opposite shows a simplified line with its concentrated components, neglecting the transverse conductance and line capacitance, with its series impedance . It is fed with the complex voltage by a generator at the beginning of the line 1 . An impedance at which the complex voltage is established is connected to the end of the line 2 . Depending on which type of load is connected, there are different operating cases: ${\ displaystyle R + \ mathrm {j} \ omega L}$${\ displaystyle {\ underline {U}} _ {1}}$${\ displaystyle X}$${\ displaystyle {\ underline {U}} _ {2}}$

• With an ohmic-inductive load , an ohmic-inductive current flows on the line . The amount of voltage on the load is always smaller than the voltage on the supplying generator.${\ displaystyle X}$${\ displaystyle {\ underline {I}} _ {12}}$
• In the case of an ohmic-capacitive load , an ohmic-capacitive current flows on the line and a higher voltage can occur on the load than on the generator.${\ displaystyle X}$${\ displaystyle {\ underline {I}} _ {12}}$

The complex voltage difference along the line is determined by the current and the series impedance, as shown graphically in the phasors in the phasors , and can be broken down into two components: A so-called series voltage in the same phase position as the voltage , which represents the so-called series voltage drop . And, in a normal position, the component of the transverse stress that expresses the transverse stress drop. The two phasors for the longitudinal and transverse voltage drop are shown in red in the phasor diagrams selected as examples. ${\ displaystyle \ Delta {\ underline {U}}}$${\ displaystyle {\ underline {I}} _ {12}}$${\ displaystyle {\ underline {U}} _ {AL}}$${\ displaystyle {\ underline {U}} _ {2}}$${\ displaystyle {\ underline {U}} _ {AQ},}$

In low and smaller medium voltage networks , the voltage drop along lines is only described with sufficient accuracy by the longitudinal voltage drop, and the transverse voltage drop can be neglected. In high-voltage networks , especially in spatially extensive interconnected networks , the transverse voltage drop plays an important role in controlling the individual node voltages and the resulting active power flows on transport lines.