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Difficulty: MediumParallel Circuits

In direct-current (DC) parallel circuit analysis, modifying circuit components or introducing faults alters electrical parameters according to fundamental circuit laws. Match each parallel circuit condition or parameter on the left with its correct electrical behavior or outcome on the right.

  • Adding an additional resistive branch across an energized parallel busDecreases the total equivalent resistance (ReqR_{\text{eq}}) and increases total current drawn from the power source.
  • Occurrence of an open-circuit fault in one branch of a multi-branch networkDrops current to zero only in the faulted branch while leaving voltage and current in all remaining branches unchanged.
  • Voltage drop across branches containing unequal resistance ratings (R1<R2R_1 < R_2)Remains identical across every branch and equals the full source voltage regardless of resistance.
  • Current division between two parallel branches of unequal resistance (R1<R2R_1 < R_2)Directs a larger current through the lower resistance branch (I1>I2I_1 > I_2) inversely proportional to resistance.

Answer

Adding a branch matches decreasing total equivalent resistance; an open branch matches dropping current to zero only in that branch; branch voltage drop matches remaining identical across all branches; unequal current division matches directing larger current through the smaller resistor.
In parallel circuits: (1) Adding branches decreases equivalent resistance and raises total current; (2) An open in one branch affects only that path; (3) Voltage is equal across all branches; and (4) Branch current is inversely proportional to resistance.

Step-by-Step Solution

1
Analyze equivalent resistance behavior when adding parallel paths.
ReqR_{\text{eq}} decreases as branches are added because 1Req=1R1+1R2+⋯+1Rn\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}.
Each added branch provides an additional path for electron flow, reducing overall opposition to current.
2
Evaluate the effect of an open circuit in an isolated parallel branch.
Current ceases in the open branch, while voltage and current across other branches remain steady.
Independent branch connections across common rails preserve full line voltage across unaffected branches.
3
Determine voltage distribution across parallel loads.
Branch voltages are identical (Vsource=V1=V2V_{\text{source}} = V_1 = V_2).
All parallel elements share the same electrical junctions.
4
Determine current division rules for unequal resistances.
Current flows inversely to resistance (I1=VR1>I2=VR2I_1 = \frac{V}{R_1} > I_2 = \frac{V}{R_2} when R1<R2R_1 < R_2).
Lower resistance paths draw greater current from the constant branch voltage.

Key Concept

Parallel Circuit Voltage, Current, Resistance, and Fault Characteristics
Estimated Time:1m 15s
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Topics

Parallel Circuits

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