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Difficulty: MediumOhm's Law

An electromagnetic security gate lock operates on an 18 V18\text{ V} direct-current (DC) power source. When fully energized, the lock draws a steady current of 250 mA250\text{ mA}. What is the electrical resistance of the lock in ohms (Ω\Omega)?

Answer: 72 Ω

Answer

The electrical resistance of the electromagnetic lock is 72 Ω72\ \Omega.
According to Ohm's Law (V=I×RV = I \times R), resistance is found by dividing the potential difference by the current (R=VIR = \frac{V}{I}). Converting 250 mA250\text{ mA} to 0.25 A0.25\text{ A} and dividing 18 V18\text{ V} by 0.25 A0.25\text{ A} yields exactly 72 Ω72\ \Omega.

Step-by-Step Solution

1
Convert the current measurement from milliamperes (mA\text{mA}) to amperes (A\text{A}).
I=250 mA=0.25 AI = 250\text{ mA} = 0.25\text{ A}
Ohm's Law calculations require current in base SI units (amperes) to yield resistance in ohms.
2
Rearrange Ohm's Law (V=I×RV = I \times R) to isolate resistance (RR).
R=VIR = \frac{V}{I}
Resistance is equal to the applied electromotive force (voltage) divided by the resulting current flow.
3
Substitute the given voltage and converted current into the formula and solve.
R=18 V0.25 A=72 ΩR = \frac{18\text{ V}}{0.25\text{ A}} = 72\ \Omega
Dividing 18 V18\text{ V} by 0.25 A0.25\text{ A} gives the total circuit resistance in ohms.

Key Concept

Ohm's Law states that resistance (RR) equals voltage (VV) divided by current (II), represented by the formula R=VIR = \frac{V}{I}.
Estimated Time:45s
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Topics

Ohm's Law

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