Voltage drop

Voltage drop is a reduction in voltage in an electrical circuit. Voltage drop, which is present in any electrical circuit powering any device, must be considered to varying degrees in circuit design. In digital electronics, a potentially damaging over-reduction in voltage is commonly referred to as voltage droop. In home wiring, voltage drop usually refers specifically to that portion of the voltage lost in the conductors supplying the circuit preceding the point at which the intended item is powered. In what follows, we generally use the term voltage drop in this restrictive sense with no loss of generality.

Fundamentals of voltage drop

A famous formula in electronics is Ohm's Law, which simply states (in one of its many possible manifestations) that electrical resistance in a circuit is equal to the voltage divided by the current. For example, a 24V circuit drawing a 3A current is said to have a resistance of 8 ohms. In wiring, the total resistance of a circuit depends not only on the resistance of the item being powered, but also on the resistance of the conductor (wiring) supplying the item. The resistance of the conductor depends upon several factors, but most notable are the composition, cross sectional radius, ambient temperature, and total length of conductor present.

Typically, voltage drop is not very important to electronics hobbyists, since the small circuits they are building have all but a tiny fraction (0.01% or less) of the total resistance in the load (e.g., a small digital circuit) to be powered. In home wiring, however, this is often not the case. For example, an electric space heater may very well have a resistance of ten ohms, and the wires which supply it may have a resistance of 0.2 ohms, fully 2% of the total circuit resistance. This means that 2% of the supplied voltage is actually being consumed by the wire itself, and the intended load (the space heater) is receiving an undervoltage. Excessive undervoltages are not only inconvenient, they may also damage delicate circuits built for specific supply voltages.

This example illustrates a fact that must be considered in different ways by everyone involved in the use of electricity, from the electricity generator, their transmission lines, your electrical service entrance, and the final wiring in the end consumer's location.

Voltage drop in direct current circuits

A voltage drop is produced when a current is forced through a conductor. The conductor may be a copper wire, or a resistive load. The voltage measured across a conductor (or one of many conductors in a circuit) is called voltage drop. Voltage (and voltage drop) is typically measured in volts, current in amperes and resistance in ohms. The relationship among these values in direct current circuits is expressed in the formula:

\mathbf{V} = \mathbf{I} \times \mathbf{R}

(a manifestation of Ohm's Law).

Voltage drop in alternating current circuits

Alternating current is a current that continually reverses direction in a circuit in sinusoidal fashion. The current used in the distribution systems of the United States alternates at 60 cycles per second (60 Hertz), while those in other parts of the world may alternate at 50 cycles per second. The voltage drop in an alternating current (AC) circuit is the product of the current and the impedance (Z) of the circuit. Impedance is analogous to resistance; impedance takes into account, however, the additional electromagnetic properties involved with alternating current loads. Electrical impedance, like resistance, is expressed in ohms and opposes current flow in a circuit. Electrical impedance is the vector sum of electrical resistance, capacitive reactance, and inductive reactance. The voltage drop occurring in an alternating current circuit is the product of the current and impedance of the circuit. It is expressed by the formula

\mathbf{E} = \mathbf{I} \times \mathbf{Z}

, analogous to Ohm's law for direct current circuits.

Minimizing voltage drop in power transmission

Great distances often occur in electric power transmission. Any power generated, but not delivered to the customer, is a financial loss. Power is lost in the conductors throughout the entire length of the transmission lines. One (very expensive) way of reducing the lost power is to increase the conductor size and thus reduce the net resistance. Another way to minimize power lost because of voltage drop is to increase the voltage. This reduces the current for a given power transmission and hence the attendant voltage drop and power loss. When we compare the two formulae for power:

\mathbf{W} = \mathbf{I} \times \mathbf{E}

and

\mathbf{W} = \mathbf{I^2} \times \mathbf{R}

it becomes evident that for a given amount of power transmitted, both the voltage drop and power loss are reduced when the current is decreased while the resistance remains constant. It is for this reason that utility supplied electrical mains are often at a very dangerous tens of thousands of volts; should the electricity have been transmitted to customers at the nominal end user voltage, the size, cost, and weight of the necessary conductors would be enormous.

Voltage drop in household wiring

In household wiring good design requires that wire size be sufficient to keep power dissipation within limits so that the wiring will not be overheated. In a given wire, the power dissipation is a function of the current. The maximum safe current for a given conductor is known as ampacity. Ampacity is independent of the length of the conductor and the supplied voltage; it has only to do with composition (for example, copper or aluminum), the radius of the conductor, and ambient conditions (such as insulating materials on the wire, ambient temperature at usage location, and so on). The circuits are protected by circuit breakers or fuses to prevent exceeding the rated ampacity. However, this is only the first consideration when selecting conductor sizes for applications.

The second consideration, often neglected by well-meaning homeowners installing their own electrical circuits, is the voltage drop for a given circuit and load. As already discussed in this article, voltage drop through a conductor depends in part upon the total net resistivity of the conductor, which in turn depends upon the total length of the conductor. Circuit loads (toasters, televisions, and so forth) have supplied to them a voltage equal to the originally induced voltage at the circuit panel (nominally 120V in North America or 220V in Europe) minus the voltage drop across the supplying conductor. The National Electric Code specifies that no more than 2% voltage drop shall be permitted in circuit wiring. While for a lightbulb a large voltage drop will result in a harmless condition of slightly less bright light being produced, incorrect voltages induced onto delicate circuitry (as for example in a DVD player, computer, and so forth) may quite easily result in an electrically damaging condition. It is quite easy to have a circuit well within the ampacity guidelines for its wiring, but whose voltage drop is too large.

For these reasons, it is wise to consult the National Electric Code (discussed below) to determine to correct sized wiring not only for the total current to be drawn, but also to insure that the net voltage drop on the conductor shall not exceed the 2% specification. This is particularly the case when running long lengths of wire (to the attic, garage, or outbuilding, for example). The NEC specifies quite precisely the lengths of circuit runs for a given wire size that will cause a 2% voltage drop for a given amperage. An outbuilding/shed at twenty meters from your circuit panel to which you intend to draw ten amps should not, for example, be serviced by 14 AWG wire (whose ampacity is nonetheless well over your ten amp intention) due to the voltage drop. In such cases, it is wise, and NEC-compliant, to use larger, more expensive 12 AWG wire.

To measure the voltage drop in a household circuit, remove all loads from the circuit, and measure the supplied voltage with a (preferably digital) volt meter. Then, plug in a household appliance which draws 10-15 amps of purely resistive load (such as a toaster, hair dryer, or space heater) and measure the voltage now present at the outlet while such a device runs. A voltage drop shall be clearly visible; if the drop exceeds 2%, your voltage drop is higher than the commonly accepted limit. For example, if an unloaded outlet shows 118V dropping to just under 117V when a space heater is applied, your voltage drop is within acceptable limits. If the same circuit shows 115V when loaded, your voltage drop is excessive.

The National Electric Code

In the United States the National Electric Code (NEC) addresses voltage drop and specifies the electrical conductor (wire) size for a variety of conditions.

External links

Electricity

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