Instrumentation

# How to do the voltage drop calculation of instrument cable?

To determine the voltage drop in an instrument cable, many factors must be considered, including the cable length, current passing through the cable, cable material, and cross-sectional area.

To determine the voltage drop, follow these simple steps:

## Determine the cable parameters

Identify the material and cross-sectional area of the instrument cable. This information is typically provided by the cable manufacturer or can be measured directly if you have access to the cable.

## Determine the length of the cable

Measure the total length of the cable run from the power source to the load. Ensure that you consider the length of both the outgoing and returning cables if applicable.

## Determine the current

Determine the current flowing through the cable. This value can be obtained from the electrical load specifications or measured using a current meter.

## Find the resistivity of the cable material

Each cable material has a specific resistivity value, which is typically provided by the manufacturer or available in reference tables. The resistivity is denoted by the Greek letter rho (ρ) and is measured in ohm-meters (Ω·m).

## Calculate the resistance of the cable:

The resistance (R) of the cable can be calculated using the formula:

R = (ρ * L) / A

where:

• R represents the resistance of the cable in ohms (Ω).
• ρ (rho) is the resistivity of the cable material in ohm-meters (Ω·m).
• L represents the length in metres (m) of the cable.
• A is the cross-sectional area of the cable in square meters (m²).

## Calculate the voltage drop:

The voltage drop (Vd) can be calculated using Ohm’s law:

Vd = I * R

where:

• Vd represents the voltage drop in volts (V).
• I is the current flowing through the cable in amperes (A).
• R represents the resistance of the cable in ohms (Ω).

Remember that, depending on the particular application, the voltage drop is typically regarded as acceptable up to a particular percentage of the nominal voltage. The allowable voltage drop limitations for your specific system should be determined by consulting any applicable standards or guidelines.

Also take note that the power factor for this computation is assumed to be one for both the DC and the AC systems. Additional considerations could be needed if your system has a lower power factor.

## Example Instrument voltage drop calculation:

We have an instrument cable made of copper with a cross-sectional area of 1.5 mm². The cable length is 50 meters, and the current flowing through the cable is 2.5 Amperes. Approximately, the resistivity of copper is 1.68 x 10-8 ohm-meters.

## Determine the cable parameters:

Cable material: Copper

Cross-sectional area (A): 1.5 mm²

## Determine the cable length:

Cable length (L): 50 meters

## Determine the current:

Current (I): 2.5 Amperes

## Find the resistivity of the cable material

Resistivity (ρ) of copper: 1.68 x 10-8 ohm-meters

## Calculate the resistance of the cable:

The cable’s internal resistance(R) = ( ρ * L ) / A

## Substituting the values:

R = (1.68 x 10-8  ohm-meters * 50 meters) / (1.5 mm²)

Since the cross-sectional area is given in mm², we need to convert it to square meters:

1.5 mm² = 1.5 x 10-6

## Substituting the converted values:

R = (1.68 x 10-8 ohm-meters * 50 meters) / (1.5 x 10-6 m²)

R = 0.56 ohms

## To Calculate the instrument cable voltage drop:

Voltage drop (Vd) = I * R

## Substituting the values:

Vd = 2.5 Amperes * 0.56 ohms

Vd = 1.4 volts

Therefore, the voltage drop across the instrument cable in this example is 1.4 volts.

Keep in mind that this is a simplified calculation, and additional factors such as temperature, cable bundling, and frequency can affect the voltage drop. If you require precise calculations, it’s advisable to consult relevant standards or use specialized software tools.

## What are the factors affecting voltage drop?

In low-voltage and low-power applications, such as the transmission of signals from sensors, instruments, or control devices, instrument cables are frequently employed. When it comes to power cables used for high-power applications, voltage drop is typically less important in these situations.

For the equipment or instrument connected to the cable to function properly, it is crucial to make sure the voltage at the receiving end stays within an acceptable range.

You would use a similar procedure to the one previously explained to determine the voltage drop in instrument cables while taking the cable length, current, and other factors into account. However, employing adequate cable diameters and keeping the cable length within acceptable ranges typically results in a small or negligible voltage drop.

Regarding instrument cable voltage drop, the following extra factors should be taken into account:

## Cable sizing

Select a cable with an adequate conductor size to minimize voltage drop. Larger conductor sizes have lower resistance, resulting in reduced voltage drop.

## Keep cable lengths short

Minimize the cable length whenever possible to reduce voltage drop. This can be achieved by locating the instrument or control devices as close as possible to the control panel or source of power.

## Consider cable impedance

Instrument cables may have impedance values that can impact the transmission of signals, especially in long cable runs. It is important to consult cable specifications and choose cables with suitable impedance characteristics for the intended application.

## Check manufacturer’s recommendations

Always refer to the cable manufacturer’s documentation or specifications for any specific voltage drop guidelines or recommendations they provide for their instrument cables.

## Consider system requirements

Consider the sensitivity of the equipment or instrument connected to the cable and ensure that the voltage drop remains within acceptable limits for proper operation. Different applications may have different voltage drop tolerance levels, so it’s important to understand the specific requirements of your system.

### Sundareswaran Iyalunaidu

With over 24 years of dedicated experience, I am a seasoned professional specializing in the commissioning, maintenance, and installation of Electrical, Instrumentation and Control systems. My expertise extends across a spectrum of industries, including Power stations, Oil and Gas, Aluminium, Utilities, Steel and Continuous process industries. Tweet me @sundareshinfohe