A technician is troubleshooting a circuit where two identical heating elements, R_1 and R_… — Armed Services Vocational Aptitude Battery (ASVAB)

A technician is troubleshooting a circuit where two identical heating elements, $R_1$ and $R_2$ , are connected in series across a $120\text{ V}$ AC supply. When the circuit is energized, neither element produces heat. Using a digital multimeter set to AC voltage, the technician measures $0\text{ V}$ across $R_1$ and $120\text{ V}$ across $R_2$ . Based on these measurements, which of the following is the most likely fault in the circuit?

A
$R_1$ has developed a short circuit.
$R_2$ has developed an open circuit.Answer
C
$R_2$ has developed a short circuit.
D
$R_1$ has developed excessive contact resistance.

Answer

The heating element

R_2

has an open circuit.

In a series circuit containing an open fault, the current drops to zero throughout the loop. According to Ohm's Law (

V = I \times R

), any intact component drops

0\text{ V}

because no current flows through it. Consequently, the entire source potential of

120\text{ V}

appears directly across the terminals of the open element (

R_2

Step-by-Step Solution

Analyze current flow in the series circuit based on operating symptoms.

Because neither series element produces heat, the total circuit current is zero (

I = 0\text{ A}

In a series circuit, any break in continuity stops current through all components.

Apply Ohm's Law to the intact component

R_1

V_{R1} = I \times R_1 = 0\text{ A} \times R_1 = 0\text{ V}

Without current flow, no potential difference develops across an intact resistor.

Evaluate the voltage drop across the faulted component

R_2

V_{R2} = 120\text{ V}

(entire supply voltage).

An open component represents infinite resistance, placing the multimeter in series with the line voltage across the open gap, thereby reading full source voltage.

Key Concept

In a series circuit, an open component prevents current flow through all other components and drops the entire applied source voltage across the open point.

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