A 4-20 mA signal is passed through a 250 Ω resistor. What voltage range is produced across the resistor, and what percentage of the ADC's input range does the 20 mA signal correspond to?

A 4-20 mA signal is passed through a 250 Ω resistor. What voltage range is produced across the resistor, and what percentage of the ADC's input range does the 20 mA signal correspond to?

• A. 0.8-4.0 V; 16-80%
• B. 1.0-5.0 V; 20-100%
• C. 0.0-5.0 V; 0-100%
• D. 1.5-6.0 V; 30-120%

Answer: (B)

When a current loop passes through a resistor, the voltage across that resistor is given by Ohm’s law: V = I × R. For 4 mA, the voltage is 0.004 A × 250 Ω = 1.0 V. For 20 mA, it’s 0.020 A × 250 Ω = 5.0 V. So the resistor develops a voltage range from 1.0 V up to 5.0 V. If the ADC’s input range is 0–5 V, then 5.0 V is full-scale (100%). The 1.0 V level is 1.0/5.0 = 20% of full scale. Therefore the signal spans 20% to 100% of the ADC range, and the 20 mA signal specifically corresponds to 100% of the ADC input range. This matches the described answer: 1.0–5.0 V across the resistor, and 20–100% of the ADC range.

When a current loop passes through a resistor, the voltage across that resistor is given by Ohm’s law: V = I × R. For 4 mA, the voltage is 0.004 A × 250 Ω = 1.0 V. For 20 mA, it’s 0.020 A × 250 Ω = 5.0 V. So the resistor develops a voltage range from 1.0 V up to 5.0 V.

If the ADC’s input range is 0–5 V, then 5.0 V is full-scale (100%). The 1.0 V level is 1.0/5.0 = 20% of full scale. Therefore the signal spans 20% to 100% of the ADC range, and the 20 mA signal specifically corresponds to 100% of the ADC input range. This matches the described answer: 1.0–5.0 V across the resistor, and 20–100% of the ADC range.