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Series-Parallel Branch Current

A public DC-circuit question showing how to reduce a series-parallel network before tracing the current through a single branch.

Question

A 12 V12\,\text{V} battery drives a circuit consisting of a 3.0 Ω3.0\,\Omega resistor in series with two 6.0 Ω6.0\,\Omega resistors that are connected in parallel with each other. What is the current through one of the 6.0 Ω6.0\,\Omega resistors?

  1. a.0.8 A0.8\,\text{A}
  2. b.1.0 A1.0\,\text{A}
  3. c.2.0 A2.0\,\text{A}
  4. d.4.0 A4.0\,\text{A}

Correct answer

B. 1.0 A1.0\,\text{A}

Full reasoning

  1. 1Combine the parallel pair first: two equal 6.0 Ω6.0\,\Omega resistors give 6.0/2=3.0 Ω6.0/2 = 3.0\,\Omega.
  2. 2The total resistance is Req=3.0+3.0=6.0 ΩR_{eq} = 3.0 + 3.0 = 6.0\,\Omega, so the battery current is I=12/6.0=2.0 AI = 12/6.0 = 2.0\,\text{A}.
  3. 3The voltage across the parallel pair is V=(2.0 A)(3.0 Ω)=6.0 VV = (2.0\,\text{A})(3.0\,\Omega) = 6.0\,\text{V}.
  4. 4Each branch then carries I=6.0 V/6.0 Ω=1.0 AI = 6.0\,\text{V}/6.0\,\Omega = 1.0\,\text{A}, consistent with the 2.0 A2.0\,\text{A} splitting equally by symmetry.

Why each choice is right or wrong

Choice A

This adds all three resistors as if they were in series (3.0+6.0+6.0=15 Ω3.0 + 6.0 + 6.0 = 15\,\Omega), ignoring the parallel connection.

Choice B

Correct. The battery delivers 2.0 A2.0\,\text{A} through the equivalent 6.0 Ω6.0\,\Omega, and that current splits equally between the identical branches.

Choice C

This is the total battery current; it assumes the full current flows through each parallel branch instead of splitting between them.

Choice D

This applies 12 V12\,\text{V} across the 3.0 Ω3.0\,\Omega series resistor alone, as if the parallel pair contributed no resistance.

Related formula

Ohm's law

V=IRV = IR

Assumptions: The resistors are ohmic, with resistance independent of current.

Two-resistor parallel combination

Req=R1R2R1+R2R_{\text{eq}} = \frac{R_1R_2}{R_1 + R_2}

Assumptions: Both resistors connect across the same two nodes.

Related topic and practice

DC CircuitsElectromagnetism Domain GuideGauss's Law and Electric FieldsGauss's Law and Sphere RadiusCreate a free account to practice

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Sources

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 2, Section 10.2: Resistors in Series and Parallel — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
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Sources last checked 2026-08-07

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