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Difficulty: HardOhm's Law

A direct current (DC) relay coil with a fixed resistance draws 30 mA30\text{ mA} when connected across an 18 V18\text{ V} power supply. When the same relay coil is connected to a different DC power supply, an ammeter measures a current flow of 75 mA75\text{ mA} through the coil. What is the voltage of the second power supply?

  1. A
    7.2 V7.2\text{ V}
  2. 45 V45\text{ V}Answer
  3. C
    4.5 V4.5\text{ V}
  4. D
    75 V75\text{ V}

Answer

45 V45\text{ V}
The correct answer is determined by using Ohm's law (R=VIR = \frac{V}{I}) to find the coil's fixed resistance from the initial state (R=18 V0.030 A=600 ΩR = \frac{18\text{ V}}{0.030\text{ A}} = 600\,\Omega) and then determining the new voltage (V=0.075 A×600 Ω=45 VV = 0.075\text{ A} \times 600\,\Omega = 45\text{ V}).

Step-by-Step Solution

1
Convert the initial current from milliamperes to amperes and calculate the resistance of the relay coil using Ohm's law (R=VIR = \frac{V}{I}).
I1=30 mA=0.030 AI_1 = 30\text{ mA} = 0.030\text{ A}; R=18 V0.030 A=600 ΩR = \frac{18\text{ V}}{0.030\text{ A}} = 600\,\Omega
The resistance of the coil remains constant regardless of the applied supply voltage.
2
Convert the second current reading to amperes and calculate the new supply voltage using Ohm's law (V=I×RV = I \times R).
I2=75 mA=0.075 AI_2 = 75\text{ mA} = 0.075\text{ A}; V2=0.075 A×600 Ω=45 VV_2 = 0.075\text{ A} \times 600\,\Omega = 45\text{ V}
Ohm's law states that the potential difference across a resistor equals current multiplied by resistance.

Key Concept

Direct proportionality between voltage and current across a fixed resistance (V=I×RV = I \times R) and metric unit conversion.
Estimated Time:45s
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Topics

Ohm's Law

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