A technician is troubleshooting a test circuit connected to a 32\text{V} DC power supply. … — Armed Services Vocational Aptitude Battery (ASVAB)

A technician is troubleshooting a test circuit connected to a $32\text{V}$ DC power supply. The circuit consists of a fixed resistor $R_1$ in series with a parallel block. The parallel block contains a $12\text{ k}\Omega$ fixed resistor and a variable resistor (rheostat) $R_v$ . The resistor $R_1$ has four color bands: Green, Blue, Red, and Gold. The technician adjusts the rheostat $R_v$ until the total current drawn from the power supply is exactly $4\text{ mA}$ .

What is the resistance setting of the rheostat $R_v$ in kilohms (k $\Omega$ )?

Answer: 3 kΩ

Answer

The total resistance required by the circuit to draw

4\text{ mA}

from a

32\text{V}

source is

8\text{ k}\Omega

. The series resistor

R_1

(Green, Blue, Red) contributes

5.6\text{ k}\Omega

. This leaves exactly

2.4\text{ k}\Omega

required for the parallel section. For a

12\text{ k}\Omega

resistor in parallel with an unknown

R_v

to yield an equivalent resistance of

2.4\text{ k}\Omega

R_v

must be set to

3\text{ k}\Omega

Step-by-Step Solution

Decode the color code of resistor

R_1

R_1 = 5.6\text{ k}\Omega

The color bands are Green (5), Blue (6), and Red (multiplier of

10^2

or 100). Thus,

56 \times 100 = 5,600\ \Omega

, which is

5.6\text{ k}\Omega

. The Gold band indicates a 5% tolerance, which applies to real-world variance but does not alter our nominal calculation.

Calculate the total equivalent resistance (

R_{eq}

) of the circuit.

R_{eq} = 8\text{ k}\Omega

Using Ohm's Law (

R = \frac{V}{I}

), divide the source voltage (

32\text{V}

) by the total current (

4\text{ mA}

0.004\text{ A}

) to find the total resistance required to draw that current.

Determine the required equivalent resistance of the parallel block.

R_{parallel} = 2.4\text{ k}\Omega

Since

R_1

is in series with the parallel block, subtract

R_1

from the total circuit resistance to find the resistance of the parallel segment:

8\text{ k}\Omega - 5.6\text{ k}\Omega = 2.4\text{ k}\Omega

Solve for the rheostat's resistance (

R_v

R_v = 3\text{ k}\Omega

The parallel block contains a

12\text{ k}\Omega

resistor and

R_v

. Using the parallel resistance formula

\frac{1}{R_p} = \frac{1}{R_a} + \frac{1}{R_b}

, we get

\frac{1}{2.4} = \frac{1}{12} + \frac{1}{R_v}

. Rearranging gives

\frac{1}{R_v} = \frac{1}{2.4} - \frac{1}{12} = \frac{10}{24} - \frac{2}{24} = \frac{8}{24} = \frac{1}{3}

, meaning

R_v = 3\text{ k}\Omega

Key Concept

Integrating Ohm's law with series-parallel equivalent resistance and resistor color code decoding.

Estimated Time:3m 0s

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