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Difficulty: HardOhm's Law Calculations and Concepts

An avionics technician tests a DC monitoring circuit connected to a constant 450 V450\text{ V} power supply. The circuit currently draws 25 mA25\text{ mA} of current. To meet new operating specifications, the current must be reduced to 9 mA9\text{ mA}. What is the required new resistance of the circuit?

  1. A
    50 Ω50\,\Omega
  2. B
    4.05 kΩ4.05\text{ k}\Omega
  3. 50 kΩ50\text{ k}\OmegaAnswer
  4. D
    20 kΩ20\text{ k}\Omega

Answer

The required new resistance of the circuit is 50 kΩ50\text{ k}\Omega.
According to Ohm's law, resistance equals voltage divided by current (R=VIR = \frac{V}{I}). Converting the target current of 9 mA9\text{ mA} to standard amperes yields 0.009 A0.009\text{ A}. Dividing the constant source voltage of 450 V450\text{ V} by 0.009 A0.009\text{ A} results in 50,000 Ω50,000\,\Omega, which simplifies to 50 kΩ50\text{ k}\Omega.

Step-by-Step Solution

1
Identify the target circuit parameters and convert metric units to base SI units
Voltage V=450 VV = 450\text{ V}, Target Current I=9 mA=9×10−3 A=0.009 AI = 9\text{ mA} = 9 \times 10^{-3}\text{ A} = 0.009\text{ A}
Ohm's law requires current to be in amperes when voltage is in volts to produce resistance in ohms.
2
Rearrange Ohm's law (V=I×RV = I \times R) to solve for resistance (RR)
R=VIR = \frac{V}{I}
Resistance is equal to the potential difference divided by the resulting current flow.
3
Calculate the target resistance and convert to kilohms
R=450 V0.009 A=50,000 Ω=50 kΩR = \frac{450\text{ V}}{0.009\text{ A}} = 50,000\,\Omega = 50\text{ k}\Omega
Dividing 450450 by 0.0090.009 gives 50,000 Ω50,000\,\Omega, which is expressed as 50 kΩ50\text{ k}\Omega using standard metric prefixes.

Key Concept

Ohm's Law for Resistance (R=VIR = \frac{V}{I}) with Metric Prefix Conversion

Alternative Method

Using direct prefix arithmetic: since volts divided by milliamperes directly yields kilohms (VmA=kΩ\frac{\text{V}}{\text{mA}} = \text{k}\Omega), calculate 450 V9 mA=50 kΩ\frac{450\text{ V}}{9\text{ mA}} = 50\text{ k}\Omega directly without manual decimal expansion.
Estimated Time:1m 15s
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Topics

Ohm's Law Calculations and Concepts

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