In direct-current (DC) circuit analysis, modifications to individual parallel paths direct… — Armed Services Vocational Aptitude Battery (ASVAB)

In direct-current (DC) circuit analysis, modifications to individual parallel paths directly impact total resistance, total current, and branch behavior. Match each parallel circuit modification on the left with its resulting electrical effect on the right.

Adding an additional resistive branch across the constant voltage supplyTotal equivalent resistance decreases, total current increases, and current through original branches remains unchanged.
Increasing the resistance value of a single existing branchTotal equivalent resistance increases, current in that specific branch decreases, and total current decreases.
Opening one branch in a multi-branch parallel networkTotal equivalent resistance increases, total current decreases, and all remaining intact branches operate normally.
Connecting a zero-resistance short circuit across one parallel branchTotal equivalent resistance drops to zero, bypassing all other parallel loads and causing an excessive current surge.

Answer

Adding an additional branch matches with decreased total resistance, increased total current, and unaffected existing branches; Increasing one branch resistance matches with decreased branch current, decreased total current, and increased total resistance; Opening one branch matches with increased total resistance, decreased total current, and normal operation of remaining branches; Connecting a short circuit matches with total resistance dropping to zero, bypassing parallel loads, and causing an excessive current surge.

In parallel circuits, each branch receives full source voltage independently. Adding branches decreases total resistance and increases total current without changing existing branch currents. Changing one branch resistance alters only that branch's current and total current. An open circuit disables only the affected branch, whereas a short circuit drops total resistance to zero across all branches.

Step-by-Step Solution

Analyze the impact of adding a parallel branch

R_{\text{eq}}

decreases and

I_{\text{total}}

increases

Each additional parallel path increases overall circuit conductance (

G_{\text{total}} = G_1 + G_2 + \dots

), lowering equivalent resistance.

Apply Ohm's law to evaluate increasing a single branch's resistance

I_{\text{branch}}

drops,

I_{\text{total}}

drops, and

R_{\text{eq}}

rises

With branch voltage fixed by the power source, current through that branch varies inversely with its resistance.

Determine the effect of an open-circuit fault in one parallel branch

Defective branch current goes to zero while intact branches continue functioning

Parallel branches are electrically independent because each branch connects directly across the full supply voltage.

Evaluate a short-circuit condition across any parallel branch

R_{\text{eq}} \approx 0\ \Omega

and total current surges drastically

A parallel short bridges the supply rails directly, shunting current away from all resistive paths.

Key Concept

Independent branch operation and equivalent resistance behavior in parallel DC circuits

Estimated Time:1m 0s

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