In a 4-20 mA DC current loop, with a 250-ohm resistor connected in parallel to a 1-5 VDC relay, if the loop current is 12 mA, what is the relay input voltage?

• A. 1 V DC
• B. 3 V DC
• C. 6 V DC
• D. 12 V DC

Answer: (B)

In a 4-20 mA loop, the current is fixed by the transmitter, and any parallel resistor turns that current into a voltage. The relay input shares the same voltage as that resistor, since they’re in parallel. If the relay’s current draw isn’t specified, we typically assume it’s small compared with the loop current, so almost all of the 12 mA flows through the 250-ohm resistor. The voltage across the resistor (and thus across the relay) is given by Ohm’s law: V = I × R = 12 mA × 250 Ω = 3 V. So the relay input voltage is about 3 V, which fits its 1–5 V DC rating. If the relay coil drew more current, the voltage would be different, but that information isn’t provided, and the 3 V result is the standard assumption.