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Difficulty: MediumOhm's Law Calculations and Concepts

An industrial temperature sensor module with a calibrated internal resistance of 4.5 kΩ4.5\text{ k}\Omega draws a steady direct current of 8 mA8\text{ mA} during normal operation. What is the voltage drop across the sensor module in volts (V\text{V})?

Answer: 36 V

Answer

The voltage drop across the sensor module is 36 V36\text{ V}.
According to Ohm's Law, voltage (VV) equals current (II) multiplied by resistance (RR). Given I=8 mA=0.008 AI = 8\text{ mA} = 0.008\text{ A} and R=4.5 kΩ=4500 ΩR = 4.5\text{ k}\Omega = 4500\text{ }\Omega, the calculation is V=0.008 A×4500 Ω=36 VV = 0.008\text{ A} \times 4500\text{ }\Omega = 36\text{ V}.

Step-by-Step Solution

1
Convert the given metric prefixes to standard base units (amperes and ohms).
I=8 mA=8×10−3 A=0.008 AI = 8\text{ mA} = 8 \times 10^{-3}\text{ A} = 0.008\text{ A} and R=4.5 kΩ=4.5×103 Ω=4500 ΩR = 4.5\text{ k}\Omega = 4.5 \times 10^{3}\text{ }\Omega = 4500\text{ }\Omega
Ohm's law requires fundamental SI units (volts, amperes, and ohms) for accurate mathematical evaluation.
2
Select the appropriate form of Ohm's Law to calculate voltage (VV).
V=I×RV = I \times R
Voltage across a resistive load equals the product of the current flowing through it and its resistance.
3
Substitute the converted values into the formula and solve.
V=0.008 A×4500 Ω=36 VV = 0.008\text{ A} \times 4500\text{ }\Omega = 36\text{ V}
Multiplying 8×10−3 A8 \times 10^{-3}\text{ A} by 4.5×103 Ω4.5 \times 10^{3}\text{ }\Omega simplifies directly to 8×4.5=36 V8 \times 4.5 = 36\text{ V} because the metric prefixes milli (10−310^{-3}) and kilo (10310^{3}) cancel each other.

Key Concept

Ohm's Law: Voltage Calculation (V=I×RV = I \times R)

Alternative Method

Recognize that the prefix multiplier milli- (10−310^{-3}) and kilo- (10310^{3}) cancel out when multiplied together: (8 mA)×(4.5 kΩ)=8×4.5 V=36 V(8\text{ mA}) \times (4.5\text{ k}\Omega) = 8 \times 4.5\text{ V} = 36\text{ V}.
Estimated Time:1m 0s
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Topics

Ohm's Law Calculations and Concepts

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