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Difficulty: MediumOhm's Law Calculations and Concepts

A technician is testing a direct current (DC) relay coil connected to a 48 V48\text{ V} power supply. An ammeter placed in series with the circuit measures a steady current of 150 mA150\text{ mA}. Based on Ohm's law, what is the internal electrical resistance of the relay coil in ohms (Ω\Omega)?

Answer: 320 ohms

Answer

The internal electrical resistance of the relay coil is 320 Ω320\text{ }\Omega.
According to Ohm's law, resistance is found by dividing voltage by current (R=VIR = \frac{V}{I}). Converting 150 mA150\text{ mA} to 0.15 A0.15\text{ A} and dividing the applied voltage of 48 V48\text{ V} by 0.15 A0.15\text{ A} yields exactly 320 Ω320\text{ }\Omega.

Step-by-Step Solution

1
Convert the current measurement from milliamperes to base amperes
I=150 mA=150×10−3 A=0.15 AI = 150\text{ mA} = 150 \times 10^{-3}\text{ A} = 0.15\text{ A}
Standard electrical calculations using Ohm's law require current in amperes.
2
Rearrange Ohm's law formula (V=I×RV = I \times R) to isolate resistance (RR)
R=VIR = \frac{V}{I}
The circuit voltage and current are known, and resistance is the required unknown quantity.
3
Substitute the given voltage and converted current into the formula and solve
R=48 V0.15 A=320 ΩR = \frac{48\text{ V}}{0.15\text{ A}} = 320\text{ }\Omega
Dividing 4848 by 0.150.15 (or multiplying 48×20348 \times \frac{20}{3}) computes the exact resistance value.

Key Concept

Ohm's law states that electrical resistance (RR) is the ratio of voltage (VV) across a component to the current (II) flowing through it: R=VIR = \frac{V}{I}.
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Ohm's Law Calculations and Concepts

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