Example 1
Connect 6.0Ω and 3.0Ω in parallel across an ideal 12V source. Find branch and total currents.
Each branch has 12V. I1=612=2.0A and I2=312=4.0A. Itotal =6.0A and Rtotal =612=2.0Ω.
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Year 11 · SACE Stage 1
Parallel circuit analysis
Find branch currents and equivalent resistance in ideal parallel networks.
Method and worked examples
Parallel branches connect between the same two junctions, so each branch has the same potential difference. Current divides between branches and recombines: Itotal =I1+I2+ … . For resistors, 1/Rtotal =R11+R21+ … . The equivalent resistance is less than the smallest individual branch resistance because adding a path allows more current at the same voltage.
Use the supply voltage to find each branch current with I=RV, then add currents. Alternatively calculate equivalent resistance first. These ideal-source questions neglect internal resistance and wire resistance. Opening one branch stops current in that branch while other intact parallel branches remain connected to the source; it does not mean every voltage or source current stays unchanged in a real non-ideal circuit.
Example 1
Example 2
Two equal 10Ω resistors are in parallel. Find equivalent resistance.
1/Rtotal =101+101=0.20Ω−1, so Rtotal =5.0Ω.
Watch out: Their voltages are equal; branch current depends on each resistance. Equal currents require equal branch resistances here.