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Zorluk: Çok zorOhm's Law Calculations and Concepts

A technician is troubleshooting a 24 V24 \text{ V} direct current (DC) control circuit. Currently, the circuit draws 8 mA8 \text{ mA} of current. In order to reduce the current draw to 2 mA2 \text{ mA} without changing the voltage source, how much additional resistance must be added in series to the existing circuit?

  1. 9 kΩ9 \text{ k}\OmegaCevap
  2. B
    12 kΩ12 \text{ k}\Omega
  3. C
    4 kΩ4 \text{ k}\Omega
  4. D
    9 Ω9 \text{ }\Omega

Cevap

The correct amount of additional resistance needed is 9 kΩ9 \text{ k}\Omega.
To find the additional resistance required, first determine the current resistance (R=24 V0.008 A=3 kΩR = \frac{24 \text{ V}}{0.008 \text{ A}} = 3 \text{ k}\Omega). Next, calculate the total target resistance needed to limit the current to 2 mA2 \text{ mA} (R=24 V0.002 A=12 kΩR = \frac{24 \text{ V}}{0.002 \text{ A}} = 12 \text{ k}\Omega). Finally, subtract the existing resistance from the target total to find the additional series resistance required (12 kΩ−3 kΩ=9 kΩ12 \text{ k}\Omega - 3 \text{ k}\Omega = 9 \text{ k}\Omega).

Adım Adım Çözüm

1
Calculate the initial resistance of the circuit.
R1=24 V0.008 A=3,000 ΩR_1 = \frac{24 \text{ V}}{0.008 \text{ A}} = 3,000 \text{ }\Omega or 3 kΩ3 \text{ k}\Omega
Ohm's Law (R=VIR = \frac{V}{I}) is used to find the existing resistance before modifications.
2
Calculate the target total resistance required to limit the current to 2 mA2 \text{ mA}.
R2=24 V0.002 A=12,000 ΩR_2 = \frac{24 \text{ V}}{0.002 \text{ A}} = 12,000 \text{ }\Omega or 12 kΩ12 \text{ k}\Omega
Ohm's Law is applied again to determine the total resistance needed for the new current requirement.
3
Determine the additional resistance needed by subtracting the initial resistance from the target total resistance.
12 kΩ−3 kΩ=9 kΩ12 \text{ k}\Omega - 3 \text{ k}\Omega = 9 \text{ k}\Omega
Resistors in series add together (Rtotal=R1+RaddedR_{total} = R_1 + R_{added}). To find the added portion, subtract the existing resistance from the total.

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Ohm's Law Calculations and Concepts
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