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Difficulty: HardOhm's Law Calculations and Concepts

An industrial control panel supplies a constant 24 V24\text{ V} DC to a sensor circuit. During normal operation, the sensor draws a current of 16 mA16\text{ mA}. Following a component degradation, the measured current rises to 64 mA64\text{ mA} at the same operating voltage. By how many ohms (Ω\Omega) has the circuit's total resistance decreased?

Answer: 1125 Ω

Answer

The circuit's total resistance decreased by 1125 Ω1125\text{ }\Omega.
According to Ohm's law, resistance equals voltage divided by current (R=VIR = \frac{V}{I}). Converting the currents to amperes gives 0.016 A0.016\text{ A} and 0.064 A0.064\text{ A}. The initial resistance is R1=24 V0.016 A=1500 ΩR_1 = \frac{24\text{ V}}{0.016\text{ A}} = 1500\text{ }\Omega, and the final resistance is R2=24 V0.064 A=375 ΩR_2 = \frac{24\text{ V}}{0.064\text{ A}} = 375\text{ }\Omega. The decrease in resistance is 1500 Ω−375 Ω=1125 Ω1500\text{ }\Omega - 375\text{ }\Omega = 1125\text{ }\Omega.

Step-by-Step Solution

1
Convert current quantities from milliamperes (mA) to amperes (A)
I1=0.016 AI_1 = 0.016\text{ A} and I2=0.064 AI_2 = 0.064\text{ A}
Ohm's law requires current to be expressed in standard SI units (amperes) to yield resistance in ohms.
2
Calculate the initial resistance using Ohm's law (R=VIR = \frac{V}{I})
R1=24 V0.016 A=1500 ΩR_1 = \frac{24\text{ V}}{0.016\text{ A}} = 1500\text{ }\Omega
Determines the baseline operating resistance of the sensor module.
3
Calculate the degraded state resistance using Ohm's law (R=VIR = \frac{V}{I})
R2=24 V0.064 A=375 ΩR_2 = \frac{24\text{ V}}{0.064\text{ A}} = 375\text{ }\Omega
Determines the lower operating resistance corresponding to the increased current draw.
4
Calculate the net difference between initial and degraded resistance
ΔR=1500 Ω−375 Ω=1125 Ω\Delta R = 1500\text{ }\Omega - 375\text{ }\Omega = 1125\text{ }\Omega
Finds the exact reduction in total circuit resistance.

Key Concept

Ohm's Law (R=VIR = \frac{V}{I}) applied to determine resistance changes in DC circuits with metric prefix conversion.
Estimated Time:1m 30s
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Topics

Ohm's Law Calculations and Concepts

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