A technician is troubleshooting a 24 \text{ V} direct current (DC) control circuit. Curren… — Armed Services Vocational Aptitude Battery (ASVAB)

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

$9 \text{ k}\Omega$ Answer
B
$12 \text{ k}\Omega$
C
$4 \text{ k}\Omega$
D
$9 \text{ }\Omega$

Answer

The correct amount of additional resistance needed is

9 \text{ k}\Omega

To find the additional resistance required, first determine the current resistance (

R = \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 \text{ mA}

(

R = \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 \text{ k}\Omega - 3 \text{ k}\Omega = 9 \text{ k}\Omega

Step-by-Step Solution

Calculate the initial resistance of the circuit.

R_1 = \frac{24 \text{ V}}{0.008 \text{ A}} = 3,000 \text{ }\Omega

3 \text{ k}\Omega

Ohm's Law (

R = \frac{V}{I}

) is used to find the existing resistance before modifications.

Calculate the target total resistance required to limit the current to

2 \text{ mA}

R_2 = \frac{24 \text{ V}}{0.002 \text{ A}} = 12,000 \text{ }\Omega

12 \text{ k}\Omega

Ohm's Law is applied again to determine the total resistance needed for the new current requirement.

Determine the additional resistance needed by subtracting the initial resistance from the target total resistance.

12 \text{ k}\Omega - 3 \text{ k}\Omega = 9 \text{ k}\Omega

Resistors in series add together (

R_{total} = R_1 + R_{added}

). To find the added portion, subtract the existing resistance from the total.

Key Concept

Ohm's Law Calculations and Concepts

Question

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Step-by-Step Solution

Key Concept

Common Mistakes

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