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Difficulty: MediumOhm's Law Calculations and Concepts

An HVAC technician is testing a motorized zone damper actuator powered by a 24 V24\text{ V} direct current (DC) power supply. An ammeter connected in series measures a current draw of 400 mA400\text{ mA} through the actuator coil. What is the electrical resistance of the actuator coil?

  1. A
    0.06 Ω0.06\text{ }\Omega
  2. B
    9.6 Ω9.6\text{ }\Omega
  3. 60 Ω60\text{ }\OmegaAnswer
  4. D
    9.6 kΩ9.6\text{ k}\Omega

Answer

The electrical resistance of the damper actuator coil is 60 Ω60\text{ }\Omega.
According to Ohm's Law, resistance is calculated by dividing the voltage across the component by the current flowing through it (R=VIR = \frac{V}{I}). Converting 400 mA400\text{ mA} to amperes yields 0.4 A0.4\text{ A}. Dividing 24 V24\text{ V} by 0.4 A0.4\text{ A} gives 60 Ω60\text{ }\Omega.

Step-by-Step Solution

1
Convert the measured current from milliamperes (mA) to base amperes (A)
I=400 mA=4001000 A=0.4 AI = 400\text{ mA} = \frac{400}{1000}\text{ A} = 0.4\text{ A}
Standard electrical calculations using Ohm's Law require current to be expressed in amperes.
2
State and apply the Ohm's Law formula solved for resistance (RR)
R=VIR = \frac{V}{I}
Resistance equals electromotive force (voltage) divided by current.
3
Substitute the known values and calculate the resistance
R=24 V0.4 A=60 ΩR = \frac{24\text{ V}}{0.4\text{ A}} = 60\text{ }\Omega
Dividing 2424 by 0.40.4 gives the coil resistance in ohms.

Key Concept

Ohm's Law (R=VIR = \frac{V}{I}) and metric prefix conversion
Estimated Time:1m 0s
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Topics

Ohm's Law Calculations and Concepts

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