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Question

Difficulty: MediumOhm's Law

An automotive diagnostic technician connects an auxiliary relay coil to a 12 V12\text{ V} direct-current (DC) power supply. An ammeter placed in series measures a current of 150 mA150\text{ mA}. What is the electrical resistance of the relay coil?

  1. A
    1.8 Ω1.8\ \Omega
  2. B
    12.5 Ω12.5\ \Omega
  3. 80 Ω80\ \OmegaAnswer
  4. D
    800 Ω800\ \Omega

Answer

The electrical resistance of the relay coil is 80 Ω80\ \Omega.
According to Ohm's law, electrical resistance is calculated by dividing voltage by current (R=VIR = \frac{V}{I}). Converting 150 mA150\text{ mA} to 0.15 A0.15\text{ A} and dividing 12 V12\text{ V} by 0.15 A0.15\text{ A} gives 80 Ω80\ \Omega.

Step-by-Step Solution

1
Convert the current from milliamperes (mA\text{mA}) to base units of amperes (A\text{A}).
I=150 mA=150×10−3 A=0.15 AI = 150\text{ mA} = 150 \times 10^{-3}\text{ A} = 0.15\text{ A}
Ohm's law requires values in standard SI base units (volts, amperes, and ohms) before performing calculations.
2
Rearrange Ohm's law (V=I×RV = I \times R) to solve for resistance (RR) and substitute the given values.
R=VI=12 V0.15 A=80 ΩR = \frac{V}{I} = \frac{12\text{ V}}{0.15\text{ A}} = 80\ \Omega
Resistance is equal to the potential difference divided by the current flowing through the component.

Key Concept

Ohm's Law states that resistance equals voltage divided by current (R=VIR = \frac{V}{I}), requiring current to be expressed in amperes.
Estimated Time:45s
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Topics

Ohm's Law

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