An electronics technician is troubleshooting a printed circuit board. The circuit original… — Armed Services Vocational Aptitude Battery (ASVAB)

An electronics technician is troubleshooting a printed circuit board. The circuit originally consisted of a DC power supply and three resistors: $R_1$ ( $100\ \Omega$ ), $R_2$ ( $150\ \Omega$ ), and $R_3$ ( $300\ \Omega$ ). $R_2$ and $R_3$ are wired in parallel with each other. This parallel pair is connected in series with $R_1$ , and the entire resistor network is connected across the power supply terminals.

To prepare for resistance testing, the technician completely removes the power supply. However, they accidentally leave a solid copper jumper wire connected across the two empty terminals where the power supply was attached.

Without desoldering any components, the technician sets a digital multimeter (DMM) to measure resistance and places the probes directly across the leads of $R_2$ . Assuming all resistors are functioning normally, what resistance reading will the DMM display?

$50\ \Omega$ Answer
B
$100\ \Omega$
C
$150\ \Omega$
D
$200\ \Omega$

Answer

The multimeter will display

50\ \Omega

because it measures the equivalent resistance of all parallel paths in the closed loop.

The multimeter measures the equivalent resistance of all parallel paths between its probes. The jumper wire connects

R_1

in parallel with the

R_2

and

R_3

branches. The equivalent resistance of

100\ \Omega

150\ \Omega

, and

300\ \Omega

in parallel is

50\ \Omega

Step-by-Step Solution

Determine the original circuit topology.

R_1

is in series with the parallel pair of

R_2

and

R_3

This establishes the baseline connections before the power supply was removed.

Analyze the effect of the jumper wire.

The jumper wire connects the open ends of the circuit, creating a closed loop. It connects the free end of

R_1

directly to the common ground/return path of

R_2

and

R_3

This fundamentally changes the topology, placing

R_1

in parallel with

R_2

and

R_3

from the perspective of the components.

Identify what the DMM measures when placed across

R_2

The DMM measures the total equivalent resistance between the two nodes of

R_2

A multimeter cannot isolate a component in a closed circuit; it reads all active parallel paths.

Calculate the equivalent resistance of the three parallel branches (

R_1

R_2

R_3

1/R_{eq} = 1/100 + 1/150 + 1/300 = 3/300 + 2/300 + 1/300 = 6/300

R_{eq} = 300 / 6 = 50\ \Omega

To find the final reading displayed by the meter.

Key Concept

In-Circuit Resistance Measurement and Component Isolation

Question

Answer

Step-by-Step Solution

Key Concept

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