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Voltage Drop: Causes, Solutions and Calculations

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voltage drop formula for cable

To calculate the voltage drop specifically for a cable in an electrical circuit, you can use the following formula:

Vd = (I * L * R * 2) / (1000 * K)

Where:

  • Vd is the voltage drop (in volts).
  • I: is the current in amperes (A) flowing through the cable.
  • L is the length of the cable in feet (ft).
  • R is the resistance of the cable material in ohms per 1000 feet (Ω/1000 ft).
  • K is the circular mils (CM) or circular mil area (CMA) of the cable’s cross-sectional area.

This formula is commonly used to calculate voltage drop in cables. Here’s how you can use it:

  1. Determine the current (I) flowing through the cable, which is the load current or the current drawn by the connected devices.
  2. Measure the length of the cable (L) in feet. If you’re working with meters, you can convert them to feet (1 meter ≈ 3.28084 feet).
  3. Find the resistance of the cable material (R) in ohms per 1000 feet. This value is typically provided in cable specifications or reference materials. It depends on the type and size of the cable.
  4. Calculate the circular mils (CM) or circular mil area (CMA) of the cable’s cross-sectional area. This involves knowing the cable’s diameter and the specific cross-sectional shape (e.g., round, flat).
  5. Plug the values into the formula to calculate the voltage drop (Vd).

Remember to consider the units consistently. The formula assumes that the length is in feet, the resistance is in ohms per 1000 feet, and the current is in amperes. The result will be in volts.

Please note that cable voltage drop calculations are important for ensuring that the voltage at the load remains within acceptable limits, especially in long cable runs or when dealing with high-current loads. Accurate voltage drop calculations are critical for proper electrical system design and performance.

Calculations of Voltage Drop Formula for Cable :

Let’s go through an example of how to calculate the voltage drop for a cable using the formula I provided earlier:

Suppose you have a 120-volt electrical circuit, and you want to calculate the voltage drop for a 100-foot length of 12-gauge copper wire (which has a resistance of approximately 1.588 ohms per 1000 feet) carrying a current of 10 amperes.

  1. Current (I): The current flowing through the cable is 10 amperes (I = 10 A).
  2. Length of Cable (L): The cable length is 100 feet (L = 100 ft).
  3. Resistance of the Cable (R): For 12-gauge copper wire, the resistance is approximately 1.588 ohms per 1000 feet. So, for 100 feet, the resistance is (1.588 Ω / 1000 ft) * 100 ft = 0.1588 ohms.
  4. Circular Mil Area (CMA): The circular mil area depends on the cable’s specific cross-sectional shape and size. Let’s assume a round cable with a CMA of 6530 circular mils.

Now, we can calculate the voltage drop (Vd):

Vd = (I * L * R * 2) / (1000 * K) Vd = (10 A * 100 ft * 0.1588 ohms * 2) / (1000 * 6530 circular mils)

Let’s calculate this step by step:

  1. 10 A * 100 ft = 1000 A*ft
  2. 0.1588 ohms * 2 = 0.3176 ohms
  3. (1000 A*ft * 0.3176 ohms) / (1000 * 6530 circular mils) = 0.0486 volts

So, the voltage drop for this 100-foot length of 12-gauge copper wire carrying a 10-ampere current is approximately 0.0486 volts or about 48.6 millivolts.

Keep in mind that this is a simplified example, and actual cable calculations may involve more complex factors, such as temperature, insulation, and frequency (for AC circuits). However, this calculation gives you a basic idea of how to estimate voltage drop in a cable for DC circuits. For more precise and detailed calculations, consult cable specification sheets and relevant electrical codes.

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