A direct current (DC) circuit consists of a 48\text{ V} power supply connected in series w… — Armed Services Vocational Aptitude Battery (ASVAB)

A direct current (DC) circuit consists of a $48\text{ V}$ power supply connected in series with three resistors: $R_1 = 12\ \Omega$ , $R_2 = 24\ \Omega$ , and $R_3 = 24\ \Omega$ . In its baseline operating state, the total circuit resistance is $R_T = 60\ \Omega$ and the circuit loop current is $I = 0.8\text{ A}$ .

Match each circuit alteration on the left to its corresponding electrical outcome on the right.

A zero-resistance jumper wire (short circuit) is placed directly across resistor $R_3$ .Total resistance decreases to $36\ \Omega$ , loop current rises to approximately $1.33\text{ A}$ , and the voltage drop across $R_3$ drops to $0\text{ V}$ .
Resistor $R_2$ burns out internally, creating an open circuit condition.Circuit current drops to $0\text{ A}$ , voltage across $R_1$ drops to $0\text{ V}$ , and the entire supply voltage of $48\text{ V}$ appears across the faulty component.
A fourth resistor with a value of $R_4 = 20\ \Omega$ is connected in series with the existing chain.Total resistance increases to $80\ \Omega$ , reducing the loop current to $0.6\text{ A}$ and the voltage drop across $R_1$ to $7.2\text{ V}$ .
The power supply voltage is increased from $48\text{ V}$ to $72\text{ V}$ while keeping all components unchanged.Total resistance remains $60\ \Omega$ , loop current increases to $1.2\text{ A}$ , and the voltage drop across $R_2$ increases to $28.8\text{ V}$ .

Answer

The correct matches pair: (1) shorting resistor

R_3

with total resistance dropping to

36\ \Omega

, current rising to

1.33\text{ A}

, and

0\text{ V}

across

R_3

; (2) an open at

R_2

with loop current dropping to

0\text{ A}

and

48\text{ V}

appearing across

R_2

; (3) adding a

20\ \Omega

series resistor with total resistance rising to

80\ \Omega

, current dropping to

0.6\text{ A}

, and

7.2\text{ V}

across

R_1

; and (4) raising the source to

72\text{ V}

with total resistance remaining

60\ \Omega

, current rising to

1.2\text{ A}

, and

28.8\text{ V}

across

R_2

Each modification directly follows the governing principles of series DC circuits. In series circuits, total resistance equals the direct sum of all individual resistances (

R_T = R_1 + R_2 + \dots + R_n

), and current is constant throughout the single loop (

I_T = \frac{V_T}{R_T}

). Short circuits eliminate individual component resistance and drop component voltage to zero while raising loop current. Open circuits eliminate current entirely and place full source voltage across the open terminals. Adding series resistance reduces current throughout the loop, and increasing source voltage increases current and all individual voltage drops proportionally.

Step-by-Step Solution

Analyze the short circuit condition across

R_3

R_T = 12 + 24 = 36\ \Omega

;

I = \frac{48}{36} \approx 1.33\text{ A}

;

V_3 = 0\text{ V}

A short circuit bypasses the component with zero resistance, eliminating its resistance from the total series sum and producing zero potential difference across itself.

Analyze the open circuit condition at

R_2

I = 0\text{ A}

;

V_1 = 0\text{ V}

;

V_3 = 0\text{ V}

;

V_2 = 48\text{ V}

An open in a series circuit interrupts the sole conductive loop, causing current to cease everywhere; infinite resistance across the open component causes the full source potential to appear across the gap.

Analyze the addition of a fourth series resistor (

R_4 = 20\ \Omega

)

R_T = 60 + 20 = 80\ \Omega

;

I = \frac{48}{80} = 0.6\text{ A}

;

V_1 = 0.6 \times 12 = 7.2\text{ V}

In series circuits, equivalent resistance is additive (

R_T = \sum R

). Increasing total resistance reduces total current according to Ohm's Law (

I = \frac{V}{R_T}

), which proportionally reduces individual component voltage drops.

Analyze the voltage source increase to

72\text{ V}

R_T = 60\ \Omega

;

I = \frac{72}{60} = 1.2\text{ A}

;

V_2 = 1.2 \times 24 = 28.8\text{ V}

Resistor values are independent of source voltage. Applying Ohm's Law with higher voltage across constant resistance yields directly proportional increases in loop current and individual voltage drops.

Key Concept

Series Circuit Governing Rules: Additive Resistance, Current Continuity, Ohm's Law, and Fault Dynamics

Estimated Time:2m 0s

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