Understanding parallel circuits

What you should be able to do

Recognize two parallel resistor branches, calculate each branch current and check the total source current and equivalent resistance.

Core Idea

Parallel branches connect between the same two circuit nodes. They therefore have the same voltage across them. Each branch current depends on that branch's resistance. At the junction, source current equals the sum of branch currents. For ideal resistors, 1/R equivalent = 1/R1 + 1/R2. Two positive resistances in parallel have an equivalent resistance smaller than either individual resistance.

Worked through

Source: 12 V DC. R1: 120 Ω. R2: 240 Ω. Branch 1: I1 = 12 V ÷ 120 Ω = 0.10 A = 100 mA. Branch 2: I2 = 12 V ÷ 240 Ω = 0.05 A = 50 mA. Source current: I total = 0.10 + 0.05 = 0.15 A = 150 mA. The larger resistance takes less current at the same voltage.

Check Equivalent Resistance

From the source's perspective: R equivalent = 12 V ÷ 0.15 A = 80 Ω. An independent two-resistor check gives: R equivalent = (120 × 240) ÷ (120 + 240) = 80 Ω. The answer is smaller than 120 Ω and 240 Ω, as expected for these two positive parallel resistances. Do not add the two resistances as if they were series.

Original Fault-Reasoning Exercise

Erase a short segment of conductor in only the 240 Ω branch on a copy of the drawing. Do not erase a shared source or return conductor. That branch is now open and carries no steady current. With the ideal source still maintaining 12 V, the intact 120 Ω branch continues to carry 0.10 A. Total source current becomes 0.10 A. Now instead erase the common source connection before the split. Both branches lose their complete connection to that source. The two erased locations produce different results. Name the location precisely rather than saying only “a wire is open.”

Practice With Answers

A second worksheet has an ideal 24 V source across two parallel resistors, 240 Ω and 480 Ω. I1 = 24 ÷ 240 = 0.10 A. I2 = 24 ÷ 480 = 0.05 A. I total = 0.15 A. R equivalent = 24 ÷ 0.15 = 160 Ω. Voltage across each branch remains 24 V in this model.

Scope And Application

Real low-voltage power distribution may have shared wiring voltage drop, output current limits, protective devices and electronic loads. One fault can affect other branches through those shared elements. The worksheet's independent-branch result assumes its ideal source and intact common connections. Do not interpret this diagram as approval to parallel arbitrary supply outputs, batteries or system circuits. It illustrates loads across one source. A real device's required polarity and voltage still matter. Components merely drawn beside one another are not necessarily parallel; trace their actual connections.

Self-Check

Voice Recap

Parallel branches share voltage. Calculate each branch current, then add them. Twelve volts across 120 ohms gives 100 milliamps; across 240 ohms it gives 50 milliamps. The source provides 150 milliamps, and the equivalent resistance is 80 ohms.

Sources