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Difficulty: MediumOhm's Law

A technician is testing a direct-current (DC) indicator lamp assembly in an armored vehicle. The lamp is connected to a 24 V24\text{ V} power supply and draws a steady current of 75 mA75\text{ mA}. What is the total electrical resistance of the lamp assembly?

  1. A
    0.32 Ω0.32\ \Omega
  2. B
    1.8 Ω1.8\ \Omega
  3. 320 Ω320\ \OmegaAnswer
  4. D
    1,800 Ω1,800\ \Omega

Answer

The total resistance of the lamp assembly is 320 Ω320\ \Omega.
According to Ohm's Law (V=I×RV = I \times R), resistance equals voltage divided by current (R=VIR = \frac{V}{I}). Converting 75 mA75\text{ mA} to 0.075 A0.075\text{ A} and dividing 24 V24\text{ V} by 0.075 A0.075\text{ A} yields 320 Ω320\ \Omega.

Step-by-Step Solution

1
Convert the measured current from milliamperes (mA\text{mA}) to base amperes (A\text{A}).
I=75 mA=751000 A=0.075 AI = 75\text{ mA} = \frac{75}{1000}\text{ A} = 0.075\text{ A}
Ohm's Law calculations require standard SI units (amperes) to yield resistance in ohms.
2
Rearrange Ohm's Law (V=I×RV = I \times R) to solve for resistance (R=VIR = \frac{V}{I}) and substitute the known values.
R=24 V0.075 A=320 ΩR = \frac{24\text{ V}}{0.075\text{ A}} = 320\ \Omega
Dividing the applied voltage by the circuit current gives the total resistance.

Key Concept

Ohm's Law defines the relationship between voltage, current, and resistance (V=I×RV = I \times R, rearranged as R=VIR = \frac{V}{I}). Current must always be converted to base amperes before computing resistance.
Estimated Time:45s
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Topics

Ohm's Law

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