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# Voltage Drop Formula

We use the concept of Voltage Drop in Electrical and Electronics Systems all the time. While in electrical (and electronic) circuits, the term Voltage Drop usually means potential difference between two points, it is also used to determine the voltage losses in the conductor. We will explore more about voltage drop in the context of electrical circuits (DC and AC Circuits) and also in current carrying conductors. Then we will take a look at the Voltage Drop Formula that helps you in determining the energy loses.

Outline

## What is Voltage Drop?

In electrical and electronic circuits, we always measure the voltage across two points, usually across a component. The difference in the voltage at these two points or across a component is known as Voltage Drop.

If you remember Ohm’s Law, the voltage across a component is directly proportional to the current and the proportionality constant is the Resistance of the component. This voltage is nothing but the voltage drop of that component.

The Voltage Drop across a component is dependent on its resistance i.e., if the resistance is high, the voltage drop is also high and if the resistance is low, then the voltage drop is also low.

While the voltage drop across a component or load determines the energy consumed by that load, we also need to consider the current carrying conductors or wires. In small systems and circuits, we often assume that the resistance of negligible and all the energy supplied by the source is consumed by the load.

This is not the case in large power system that carry voltage over large distances. We cannot ignore the resistance of the conductor. Consider a large motor running in your garden and you use a long cable from the outlet to the motor.

If there is a significant voltage drop in the wire, there isn’t enough juice to run the motor and as a result, it might run hotter than normal. We can also apply the same explanation to other powerful devices such as heaters, lights and many more. An excessive voltage drop in the conductor may lead to flickering lights and heater not heating properly.

### What Causes Voltage Drop?

It is practically impossible to have zero voltage drop in the conductors as there is a slight resistance even in the purest of conductors. But what are some of the other causes of voltage drop and how can we reduce it? Let us see the answer to that.

• One of the main causes of voltage drop is the type of material used for the conductor. Copper and aluminum are two of the top choices of electrical conductors on a large scale (gold and silver are used on a micro scale). While both these are good conductors, copper is slightly a better conductor of electricity than aluminum. So, for the same size, an aluminum conductor tends to have higher voltage drop than a copper conductor.
• Next is the diameter of the conductor. Larger dimeter conductors usually have less voltage drop than smaller diameter conductors.
• A critical factor that results in a voltage drop is the length of the conductor. Longer conductors have higher voltage drop than a short conductor, assuming both the conductors are of the same diameter.
• Temperature also plays an important role on voltage drop. An increase in temperature will cause the resistance of the conductor to increase. From Ohm’s Law, we know that large resistance means more voltage drop.

Reducing voltage drop in conductors is very important as you can significantly reduce the energy wastage and also lessen your utility bill. From the above discussion, it is clear that there are several factors that cause a voltage drop in conductors. But here are some more reasons to reduce voltage drop.

• Using large conductor for larger loads will have a ow voltage drop. Even though a large conductor costs more than a regular one, you get easily paid off in terms of the overall energy saving.
• You can increase the performance of the device such as motors, heaters and lights with less voltage drop.
• It will be very easy for diagnosing errors and faults in wiring as we can easily identify the one part the circuit that has significantly higher voltage drop than the rest of the system.

## Voltage Drop Formula

It is clear that we need to properly determine the voltage drop of the conductor so that wire of correct size, diameter, length and current carrying capacity is selected for proper operation of loads such as lights, motor, heater etc.

To determine the voltage drop of a conductor, we can make use of the following Voltage Drop Formulae. Note that there is a separate voltage drop formula for a single-phase applications and also one for three phase applications.

### Single Phase Applications

The voltage drop formula for a copper conductor in single phase applications is given below:

VD = (2 x K x L x I) / cmil

Where VD is the Voltage Drop

K is Ohm-cmil per feet (Electrical Resistivity of the conductor, which is a constant)

L is length of conductor in feet

Cmil is the circular mil area of the conductor

K in the above equation is a constant known as the electrical conductivity of the conductor. You can calculate electrical resistivity K using the formula

K = (electrical resistance x cross-sectional area) / longitudinal length

For Copper, the value of K is 12.9 Ω-cmil/ft. at 75oC and for Aluminum, the value of K is 21.2 Ω-cmil/ft. at 75oC.

### Three Phase Applications

The voltage drop formula for three phase applications is very similar to that of the single-phase formula.

VD = (1.73 x K x L x I) / cmil

All the parameters are same as earlier.

## Voltage Drop Formula for Circuits

The voltage drop formulas we saw earlier are for calculating voltage drop in a conductor. But what if you want to calculate voltage drop in a circuit. We have formulas for those as well. Let us now see the voltage drop formulae in DC as well as AC Circuits.

### In DC Circuits

To calculate the voltage drop of a conductor in a small DC circuit, you can simply use the Ohm’s Law.

V = I x R

Where V is the voltage drop

I is the current in Amps

R is the electrical resistance in Ohms (Ω)

### In AC Circuits

Calculating voltage drop in AC circuits slightly different as you need to take reactance part of the conductor into consideration along with the resistance. Hence, instead of just resistance, we use impedance in AC circuits.

Z = R + jX

Where Z is the impedance

R is the resistance

X is the Capacitive and inductive reactance

Now the voltage drop in AC circuits is E = Z x I.

## Conclusion

Voltage Drop is an important calculation in electrical and electronic systems as it determines the amount of voltage dropped in the conductor rather than being delivered to the load. This voltage drop in the conductor is essentially a wasted energy that we have to pay for. You can use the voltage drop formula to determine the voltage drop in a conductor of certain diameter, length and material.