Parallel circuits — do they function as current dividers by definition?

Difficulty: Easy

Correct Answer: True

Explanation:


Introduction / Context:
Recognizing series vs. parallel behaviors helps you quickly analyze networks. This question focuses on the current-divider role of a parallel connection and how current distributes based on branch impedances.


Given Data / Assumptions:

  • Multiple resistive branches connected between the same two nodes of a source.
  • Linear, time-invariant behavior under steady-state operation.


Concept / Approach:
In parallel, all branches share the same voltage. Currents in the branches depend on their individual resistances or impedances: Ik = V / Rk for resistors. The total source current is the sum of branch currents, so the parallel network divides the incoming current among the available paths according to admittance ratios. This is precisely the definition and practical utility of a current divider.


Step-by-Step Solution:

Write total current: Itot = Σ (V / Rk) = V * Σ (1 / Rk).Branch current for two-branch case: I1 = Itot * (R2 / (R1 + R2)), I2 = Itot * (R1 / (R1 + R2)).Observe inverse dependence: smaller resistance pulls a larger share of the current.Extend to impedances for AC: use complex values and the same divider principle with admittances.


Verification / Alternative check:
Measure with an ammeter in each branch and compare with calculated divider ratios; experimental values match predictions within component tolerances.


Why Other Options Are Wrong:

  • “False” would deny the fundamental current-splitting property that distinguishes parallel from series, where voltage divides instead.


Common Pitfalls:
Swapping voltage and current divider formulas; remember: series → voltage divider, parallel → current divider.


Final Answer:
True

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion