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Difficulty: MediumOhm's Law

A technician is servicing a communications shelter ventilation fan controller that operates on a 48 V48\text{ V} direct-current (DC) power supply. A diagnostic test shows that the control circuit's primary sensing resistor has a resistance of 1.2 kΩ1.2\text{ k}\Omega. What is the current flowing through this resistor?

  1. A
    25 mA25\text{ mA}
  2. 40 mA40\text{ mA}Answer
  3. C
    400 mA400\text{ mA}
  4. D
    57.6 mA57.6\text{ mA}

Answer

40 mA40\text{ mA}
According to Ohm's Law, current is calculated by dividing voltage by resistance (I=VRI = \frac{V}{R}). First converting 1.2 kΩ1.2\text{ k}\Omega to 1200 Ω1200\ \Omega gives I=48 V1200 Ω=0.04 AI = \frac{48\text{ V}}{1200\ \Omega} = 0.04\text{ A}, which is equivalent to 40 mA40\text{ mA}.

Step-by-Step Solution

1
Convert the resistance value from kilohms (kΩ\text{k}\Omega) to base ohms (Ω\Omega).
R=1.2 kΩ=1.2×1000 Ω=1200 ΩR = 1.2\text{ k}\Omega = 1.2 \times 1000\ \Omega = 1200\ \Omega
Standard electrical calculations using Ohm's Law require base units of volts, amperes, and ohms.
2
Apply Ohm's Law (I=VRI = \frac{V}{R}) to solve for the circuit current.
I=48 V1200 Ω=0.04 AI = \frac{48\text{ V}}{1200\ \Omega} = 0.04\text{ A}
Current equals voltage divided by resistance.
3
Convert the current in amperes to milliamperes (mA\text{mA}).
0.04 A×1000 mA/A=40 mA0.04\text{ A} \times 1000\text{ mA/A} = 40\text{ mA}
The answer choices are expressed in milliamperes.

Key Concept

Ohm's Law (I=VRI = \frac{V}{R}) and metric prefix conversions
Estimated Time:45s
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Topics

Ohm's Law

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