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
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.
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.
Parallel circuit analysis practice | Year 11 Physics | Ascent Arcade