Branch current from known source: A parallel circuit has a total resistance of 50 Ω and draws 120 mA in total. What is the approximate current through a 270 Ω branch resistor?

Introduction / Context:
In parallel circuits, knowing the total resistance and total current allows you to find the source voltage. Once the source voltage is known, the current in any branch can be found using Ohm's law for that branch. This workflow is a standard analysis technique.

Given Data / Assumptions:

• Total resistance R_total = 50 Ω.
• Total current I_total = 120 mA = 0.12 A.
• One branch resistor R_branch = 270 Ω.
• Assume ideal components; all branches share the same source voltage.

Concept / Approach:

First, find the source voltage via V_source = I_total * R_total. Then apply I_branch = V_source / R_branch to obtain the branch current. This two-step method exploits the properties of parallel circuits and Ohm's law.

Step-by-Step Solution:

Verification / Alternative check:

Back-check power: P_branch ≈ V^2 / R = 36 / 270 ≈ 0.133 W. The magnitude is reasonable for a small resistor at low voltage.

Why Other Options Are Wrong:

120 mA is the total current, not a branch value. 220 mA exceeds the total available. 50 mA and 2.2 mA do not satisfy V = 6 V across 270 Ω.

Common Pitfalls:

Forgetting to compute the source voltage first, or mistakenly applying series rules to a parallel network.

Final Answer:

22 mA