Wiring, Cables and Voltage Drop

Worked example: a 10 m run to a valve manifold

A 2 A load at the end of a 10 m cable:

With 0.75 mm² the drop is 0.92 V (3.8 %), usually acceptable. A common guide is to keep the total drop below about 5 %, and above the device’s minimum voltage. Copper resistance also rises with temperature, by about 0.4 % per °C: at 60 °C the resistance is 1.16 times its value at 20 °C, and the drop for 0.75 mm² rises to 1.06 V. This covers voltage drop only: the cable must also be rated for the current, the installation method and the protective device (below).

Worked example: longest run for 5 % at 2 A

• Use the device’s limit, not just 5 %. A sensor that works down to 19.2 V (80 % of 24 V) on a 24 V supply can tolerate a drop of 4.8 V; at 2 A over 0.75 mm² that is a run of up to 52 m. Check the supply’s tolerance too: a supply that is set 1 V low leaves less.
• Increase the conductor size for long runs, or put a second supply near the load; do not add a bigger breaker.
• Loads that start in a pulse (a solenoid, a motor brake) draw more than their steady current: calculate with the peak.
• Remember the return conductor: the factor 2 in the formula is the out-and-back path.

Worked example: derating

• A 2.5 mm² copper cable with a base capacity of about 24 A (illustrative) is run in a duct at 40 °C ambient (derating factor 0.87) together with several other loaded circuits (factor 0.70): 24 × 0.87 × 0.70 = 14.6 A.
• A 20 A breaker would not protect it any more: choose a 13 or 16 A device, or a larger cable (a 4 mm² cable with a base capacity of about 32 A carries 32 × 0.87 × 0.80 = 22 A in a similar duct, enough for the 20 A motor circuit of the power page). The tables of IEC 60364-5-52 or the local code give the real numbers; the lesson is that the capacity in a hot, crowded duct is well below the free-air figure.
• For a 5 A load the thinnest cable that satisfies the drop and the rating is chosen; check both.

Worked example: how much loop resistance is allowed?

• A 24 V supply, a transmitter that needs 12 V and a 250 Ω input resistor (the input then reads 1.0 to 5.0 V): R_loop,max = (24 − 12 − 250 × 0.02) ÷ 0.02 = 350 Ω of cable and any other devices in the loop.
• A 0.75 mm² cable has a loop resistance of about 45.87 Ω per kilometer of run, so the cable could be up to about 7.6 km long: cable resistance is rarely the limit for 4–20 mA; noise and the other devices in the loop are.
• A 500 Ω input resistor (for a 2 to 10 V input) cuts the allowance to 100 Ω; an indicator, a barrier or an isolator in the loop uses some of it (check their voltage drops).
• A broken wire reads 0 mA, below the 4 mA live zero, so the system can tell a fault from a low reading (see the NAMUR note in Sensors, Signal Conditioning and ADCs). Convert the readings with the Analog Scaling Tool.

Worked example: the weight of copper

A 100 m run of a 4-core 1.5 mm² cable holds 4 × 1.5 × 100 = 600 cm³ of copper, which is 5.4 kg at a density of 8.96 g/cm³, before insulation and sheath. This is worth knowing for tray loading and scrap value, but more to the point it is why the cable bill rises quickly with section and length: stepping up a size for a long run costs real money, so place the supply or the I/O close to the load where possible (see System Architecture and Component Selection).

Worked example: how many wires in a conduit?

• Codes limit the fill of a conduit or duct to about 40 % of its cross-section for three or more wires, so that heat can escape and wires can be pulled. A 20 mm conduit has a section of 314 mm², giving 126 mm² of wire space.
• A 1.5 mm² wire with its insulation is about 3.0 mm across (7.1 mm²): 17 wires. A 2.5 mm² wire (4.2 mm, 13.9 mm²) allows only 9. In bunched cables the derating of the previous section also applies.
• Wire ducts in panels are filled to about 50 to 70 % at most, with room for additions.
• Bend radius: for an 8 mm cable, a fixed installation needs about 4 × the diameter = 32 mm; a cable that is flexed occasionally about 10 × = 80 mm; a drag-chain cable about 7.5 × = 60 mm (follow the cable maker’s figure). Bending tighter shortens the life and breaks strands.

Worked example: an Ethernet run

Twisted-pair Ethernet (100BASE-TX and 1000BASE-T) allows a maximum channel length of 100 m, including the patch cords at each end. With two 10 m patch cords that leaves 80 m of fixed cable. Beyond that use a switch, a media converter or fiber. Fiber has no electrical noise problem and no earth loops, and runs for hundreds of meters to kilometers. Keep Ethernet at least 200 mm from power cables or in a separate screened duct, and do not run a drive’s motor cable beside it (see Grounding, Shielding and Noise). The protocols and addressing are in Industrial Communication.