Enter the one-way length (m), the conductor resistance per unit length (Ω/m), and the current (amps) into the Relay Burden Calculator. The calculator will evaluate the Relay Burden (VA).
Related Calculators
- Loop Resistance Calculator
- Impedance to Voltage Calculator
- Current Imbalance Calculator
- Secondary Voltage Calculator
- All Physics Calculators
Relay Burden Explained
Relay burden is the amount of apparent power required to push current through the relay wiring loop. In this calculator, the burden comes from the resistance of the conductors between the source and the relay and back again. That means burden increases when the run gets longer, the wire resistance per unit length gets higher, or the current increases.
This is especially useful when checking whether lead resistance is adding too much load to a protection or control circuit. Even if the relay itself is suitable, excessive wiring burden can still reduce performance margin.
| Input | Meaning | Typical Units | Effect on Burden |
|---|---|---|---|
| Length | One-way conductor distance from source to relay | m or ft | Linear increase |
| Resistance per unit length | Wire resistance for each meter or foot of conductor | Ω/m or Ω/ft | Linear increase |
| Current | Circuit current carried by the relay loop | A or mA | Squared increase |
| Relay Burden | Apparent power required by the conductor loop | VA or mVA | Calculated result |
Relay Burden Formula
RB = 2DRI^2
- RB = relay burden in volt-amperes (VA)
- D = one-way length of the run
- R = conductor resistance per unit length
- I = current in amperes
The factor of 2 accounts for the full circuit path: one conductor out to the relay and one conductor back. If you already use the total loop length, do not multiply by 2 again.
Why Current Has the Biggest Impact
Current is squared in the formula, so burden grows much faster with current than with length or conductor resistance. If current doubles, the burden becomes four times larger. If current triples, the burden becomes nine times larger. This is why even modest increases in current can create a large change in required VA.
Rearranged Forms
If you know any three variables, you can solve for the fourth.
I = \sqrt{\frac{RB}{2DR}}D = \frac{RB}{2RI^2}R = \frac{RB}{2DI^2}Example
For a one-way length of 50 m, conductor resistance of 0.008 Ω/m, and current of 3 A:
RB = 2(50)(0.008)(3^2) = 7.2\ \text{VA}The wire loop alone contributes 7.2 VA of burden. If the circuit also includes additional devices, terminals, or instrumentation, those loads must be considered separately to estimate total circuit burden.
How to Use the Calculator Correctly
- Enter the one-way cable length, not the round-trip loop length.
- Enter conductor resistance in matching distance units, such as Ω/m with meters or Ω/ft with feet.
- Enter the operating current in A or mA.
- Calculate the missing value and confirm that the result is expressed in VA or mVA as needed.
Unit Notes
Consistent units are critical. A correct formula with mixed units still produces a wrong answer.
1\ \text{ft} = 0.3048\ \text{m}1\ \text{mA} = 0.001\ \text{A}1\ \text{mVA} = 0.001\ \text{VA}If a wire specification is given per 1000 ft or per km, convert it to the calculator’s selected unit basis before solving.
Practical Design Considerations
- Longer runs increase burden linearly. Doubling cable length doubles the conductor burden.
- Higher-resistance wire increases burden linearly. Smaller conductors generally have higher resistance per unit length.
- Temperature matters. Conductor resistance rises as temperature rises, so real-world burden can be higher than a room-temperature estimate.
- Wire burden is not always the entire burden. Relay inputs, test switches, terminal blocks, and other connected devices may add additional load.
- Check system limits. If the calculated burden is high, compare the total circuit burden against the rating of the associated relay or instrument transformer.
Common Mistakes
- Using total loop length and still keeping the factor of 2 in the equation.
- Entering total conductor resistance instead of resistance per unit length.
- Mixing meters with Ω/ft or feet with Ω/m.
- Forgetting that current is squared.
- Ignoring added resistance from connectors, switches, or aging conductors.
Frequently Asked Questions
Why is burden shown in VA?
Relay burden is commonly expressed as volt-amperes because it represents the load seen by the circuit. For a purely resistive lead loop, the numerical result also matches the familiar I2R power relationship.
What does one-way length mean?
One-way length is the physical distance from the source to the relay. The formula itself handles the return path with the multiplier of 2.
Does this calculate total relay circuit burden?
No. This calculator estimates the burden caused by the conductor run. If you need total burden, add the burden of the relay input and any other connected components to the wire burden.
How can burden be reduced?
Typical ways to reduce burden are shortening the cable run, using lower-resistance conductors, or lowering current where the design allows. Because current is squared, reducing current has the largest effect.
