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Electrical Basics for Instrument Technicians

Most instrument faults are electrical: a loop that can't reach 20 mA, a solenoid that won't pull in at the end of a long cable, the wrong resistor in a panel. These are the few laws you use every day, with calculators to check them.

Work on live circuits only when you are trained and authorised, with isolation and permit procedures. In hazardous areas, intrinsic-safety and other protection rules come first.

Ohm's law and power

V = I · R P = V · I = I² · R = V² / R

Know any two of voltage, current, resistance and power and you can find the others. Classic example: a 250 Ω resistor in a 4–20 mA loop gives 1–5 V (20 mA × 250 Ω = 5 V) and dissipates only 0.1 W.

Series and parallel

  • Series resistances add: R = R1 + R2 + … The same current flows through each.
  • Parallel: 1/R = 1/R1 + 1/R2 + … The total is always smaller than the smallest resistor. Two equal resistors in parallel give half the value.
  • Voltage divider: Vout = Vin · R2 / (R1 + R2), used to scale voltages for an input card (as long as the input doesn't load it).

The 4–20 mA loop budget

A two-wire transmitter needs a minimum voltage across its terminals (often 10–12 V, more with HART or displays). Everything else in the loop eats voltage at 20 mA:

Transmitter 12 V min 250 Ω → 5 V IS barrier ≈ 8 V cable margin 0 V24 V supply Max loop resistance = (Vsupply − Vmin) / 0.020 A, e.g. (24 − 12) / 0.02 = 600 Ω for everything outside the transmitter
At 20 mA each part takes its share of the 24 V supply. If the margin goes negative the loop can't reach 20 mA.

The Loop Load Check app does this budget for you.

Cable voltage drop

Long runs to solenoids, heaters or 24 V field devices lose voltage in the cable:

DC / single-phase: ΔV = 2 · L · I · R three-phase: ΔV = √3 · L · I · R R (copper, 20 °C) = 0.01724 / A Ω per metre (A in mm²), about 20 % higher at 70 °C

Example: a 2 A solenoid 150 m away on 1.5 mm² copper loses about 8 V of a 24 V supply (34 %), so it may not pull in. Use a larger cable, a shorter run or a higher supply voltage. Typical limits are 3–5 % for power circuits.

Three-phase power

S = √3 · V(line-line) · I P = S · cos φ motor shaft power = P · efficiency

A 15 kW motor at 400 V, power factor 0.85 and 100 % efficiency draws about 25.5 A per phase; with a real efficiency of 90 % it is about 28 A.

Resistor colour code

Through-hole resistors carry colour bands (IEC 60062): two or three digits, a multiplier and a tolerance band; a sixth band gives the temperature coefficient. Remember the digit order black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold ×0.1 / ±5 %, silver ×0.01 / ±10 %. Example: yellow-violet-red-gold = 4.7 kΩ ±5 %. SMD parts use codes instead: "472" = 4.7 kΩ, "4R7" = 4.7 Ω.

Live calculators

Both also work offline in the Instrument Apps Hub (Electrical Calculator, Resistor Color Code).

Electrical calculator

Resistor colour code

Q&A quiz

Related: Transmitters & Signals · Loop Checking · 4–20 mA Current Loop animation