Parallel Resistor Currents: The Same Voltage Does Not Mean Equal Current

Ideal resistors connected between the same two nodes have the same voltage across them. Each branch current is Ii = V/Ri, and the total current is the sum of the branch currents.

Identify common nodes, not just a parallel drawing

Components are electrically parallel when both ends connect to the same pair of nodes. A drawing’s visual layout can be misleading. Trace the connections and label the common voltage before calculating any current.

For positive resistances, a lower-resistance branch carries more current at that common voltage. Equal currents occur only when the branch resistances are equal under this ideal model. The sum rule follows from charge conservation at the junction.

Worked two-branch circuit

Ideal 6 Ω and 3 Ω resistors are connected in parallel across 12 V. The 6 Ω branch carries 12/6 = 2 A. The 3 Ω branch carries 12/3 = 4 A. Total source current is 2 + 4 = 6 A.

The equivalent resistance is V/Itotal = 12/6 = 2 Ω. Check with the reciprocal rule: 1/Req = 1/6 + 1/3 = 1/2, so Req = 2 Ω. It is smaller than either branch resistance, as expected for two positive parallel branches.

What changes when a branch is added?

At a fixed ideal source voltage, adding another positive-resistance branch adds another positive current. It therefore reduces equivalent resistance and increases total current. The current in an unchanged branch remains V/R for that branch in this fixed-voltage model.

A real source can have internal resistance and voltage sag. Do not generalize the ideal fixed-voltage result to every battery or supply without checking those additional effects. This guide concerns paper circuits with the assumptions stated in the question.

Common mistake

Do not divide the source voltage equally among parallel branches; that is a different series situation. Do not add the branch resistances directly either. You can avoid a reciprocal mistake by calculating each branch current first and then using Req = V/Itotal as an independent check. No practical wiring or mains experiment is proposed here.

Parallel mein voltage same; har branch ka current V/R se alag nikalo.

Three practice questions with worked answers

1. Two 4 Ω resistors are parallel across 8 V. Find branch and total currents.

   Each branch current is 8/4 = 2 A. Total current is 2 + 2 = 4 A.

2. Find the equivalent resistance of 6 Ω and 12 Ω in parallel.

   1/Req = 1/6 + 1/12 = 1/4, so Req = 4 Ω.

3. Branches of 10 Ω and 5 Ω have the same 20 V. Find their current ratio.

   Currents are 2 A and 4 A. The 10 Ω branch to 5 Ω branch ratio is 1:2.

Related study guides

• Electricity Class 10 Notes: Ohm’s Law, Series and Parallel, Heating Effect Numericals
• Ohm’s Law Numericals: Current, Voltage, Power and Energy

Need one step explained? Open the DoubtPay study tool. Check the current credit price before requesting a paid answer, and verify the working yourself.

References and authorship

Original examples and practice questions, prepared with AI assistance and editorial arithmetic review. Related definitions and methods: OpenStax: Resistors in Series and Parallel. No textbook or exam-board affiliation is claimed.