Question

Difficulty: MediumParallel Circuits

In direct-current (DC) parallel circuit troubleshooting and analysis, changes in circuit configuration directly affect voltage, current, and equivalent resistance. Match each circuit condition or modification with its corresponding electrical effect.

  • Adding an additional resistive branch in parallel to an operating circuitDecreases the overall equivalent resistance and increases the total current drawn from the source
  • Opening (disconnecting) one branch in a three-branch parallel networkReduces total circuit current while voltage and current in remaining branches remain unchanged
  • Connecting branches with unequal resistance values across a single DC sourceCauses branches with lower resistance to draw higher current while branch voltages remain equal
  • Measuring voltage drops across different parallel branchesYields identical potential difference readings across every individual branch

Answer

Adding a parallel branch matches with decreasing overall equivalent resistance and increasing total current; opening one branch matches with reducing total current while remaining branches stay unchanged; connecting unequal branches matches with lower resistance branches drawing higher current; measuring voltage drops matches with identical potential difference readings across every branch.
In parallel DC circuits, adding a branch reduces total resistance and increases total current, opening a branch isolates only that path while others continue operating normally, current divides inversely with branch resistance under constant voltage, and voltage is identical across every parallel branch.

Step-by-Step Solution

1
Analyze the effect of adding a parallel branch to an active circuit
Equivalent resistance decreases and total current increases
Every additional parallel path offers a new route for electron flow, reducing the total opposition to current.
2
Analyze the effect of an open fault in a single branch of a parallel network
Total current drops while other branches continue normal operation
Parallel branches are electrically independent across the supply rails, so opening one branch subtracts only its individual branch current from the total.
3
Determine how current distributes across branches with different resistances
Current divides inversely with resistance
With uniform branch voltages, Ohm's law (I=VRI = \frac{V}{R}) ensures that smaller resistances allow larger branch currents.
4
Verify voltage characteristics across parallel circuit elements
Voltage drop across every branch equals the source voltage
All parallel branches connect directly across the common positive and negative power distribution rails.

Key Concept

Fundamental operational principles of parallel circuits: equal branch voltage, independent branch currents, and reciprocal equivalent resistance
Estimated Time:1m 0s
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