In a parallel circuit every branch is connected across the same two nodes, so each branch sees the same voltage. The branch currents are set by their own resistances and add to form the total current drawn from the source.
Equivalent resistance
Two parallel branches
Problem. A 12 V source feeds 6 Ω and 4 Ω in parallel. Find the branch currents, the total current and the equivalent resistance.
Solution. I1 = 12 ÷ 6 = 2 A and I2 = 12 ÷ 4 = 3 A, so I_total = 5 A. 1 ÷ R_total = 1/6 + 1/4 = 5/12, therefore R_total = 12 ÷ 5 = 2.4 Ω. Check: 12 V ÷ 2.4 Ω = 5 A.
Why a parallel branch lowers resistance
Each extra branch provides another path for charge. The total current grows for the same voltage, which is exactly what a lower equivalent resistance means. This is why loads in a building or a vehicle are wired in parallel: each can operate independently at the supply voltage.
- Voltage is the same across every parallel branch.
- Branch currents add to the total source current.
- Equivalent resistance is always smaller than the smallest branch.
- Opening one branch does not stop the others; a shorted branch affects all of them.
- Parallel branches share the same voltage.
- Total current is the sum of branch currents.
- Reciprocals add for parallel resistance.
- Equivalent resistance is below the smallest branch resistance.
Worked example
Three 12 Ω branches in parallel: 1/R = 3/12, so R = 4 Ω. At 12 V the total current is 3 A, and each branch carries 1 A.