Equal resistors in parallel — current sharing: When two resistors of equal value are connected in parallel across the same source, will they carry identical currents? Choose the correct statement.

Introduction / Context:Equal-value components in parallel provide symmetry that simplifies mental math. Recognizing identical current sharing under equal resistances allows quick sizing of components and cables, and it is frequently tested in introductory circuits.

Given Data / Assumptions:

• Two resistors R and R in parallel.
• Both see the same node-to-node voltage V.
• Ideal components; wiring drops are negligible.

Concept / Approach:By Ohm’s law, I_1 = V/R and I_2 = V/R. With equal R values and equal voltage across branches (parallel connection), the branch currents are identical. The total current is I_total = I_1 + I_2 = 2 * (V/R), and each branch shares half of the total in this symmetric case.

Step-by-Step Solution:

Verification / Alternative check:In practice, tiny tolerance differences cause small current imbalance, but for idealized problems and matched parts, currents are equal. Lab measurements with 1% resistors often confirm near-equal currents within tolerance.

Why Other Options Are Wrong:

• Incorrect: Contradicts Ohm’s law under equal R and equal V.
• Only true if the source is ideal: Minor source resistance does not break symmetry significantly for concept checks.
• Only true below 1 A: The rule is not current-magnitude dependent.
• Only true at DC, not AC: For purely resistive branches, AC RMS currents remain equal as well.

Common Pitfalls:Confusing practical tolerance effects with ideal analysis; assuming identical current sharing requires equal wire lengths or identical physical layout (it does not at the conceptual level).

Final Answer:Correct