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Difficulty: EasyOhm's Law Calculations and Concepts

An automotive technician tests a 12 V12\text{ V} direct current (DC) circuit powering an auxiliary cooling fan. If the multimeter measures a current of 3 A3\text{ A} flowing through the fan motor, what is the electrical resistance of the motor?

  1. A
    36 Ω36\text{ }\Omega
  2. B
    0.25 Ω0.25\text{ }\Omega
  3. 4 Ω4\text{ }\OmegaAnswer
  4. D
    9 Ω9\text{ }\Omega

Answer

4 Ω4\text{ }\Omega
According to Ohm's law, resistance equals voltage divided by current (R=VIR = \frac{V}{I}). Dividing 12 V12\text{ V} by 3 A3\text{ A} yields 4 Ω4\text{ }\Omega.

Step-by-Step Solution

1
Identify the known values and target quantity from Ohm's law.
Voltage (VV) = 12 V12\text{ V}, Current (II) = 3 A3\text{ A}, Resistance (RR) = unknown.
Setting up the given parameters ensures the proper mathematical formula is selected.
2
Rearrange Ohm's law (V=I×RV = I \times R) to solve for resistance (RR).
R=VIR = \frac{V}{I}
Dividing both sides by current isolates resistance as the subject.
3
Substitute the measured values into the formula and calculate.
R=12 V3 A=4 ΩR = \frac{12\text{ V}}{3\text{ A}} = 4\text{ }\Omega
Carrying out the division gives the total electrical resistance of the fan motor.

Key Concept

Ohm's Law: R=VIR = \frac{V}{I}
Estimated Time:45s
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Topics

Ohm's Law Calculations and Concepts

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