In a parallel DC circuit, which statement is true?

In a parallel DC circuit, which statement is true?

• A. The voltage across each branch is different from the source
• B. The total current is equal to the sum of the currents through the individual branches
• C. The total resistance is greater than any individual branch
• D. Currents in each branch are identical

Answer: (B)

In a parallel DC circuit, the current that leaves the source splits among the branches and then recombines, so the total current equals the sum of the currents in each branch. The voltage across every branch is the same as the source, which is why the statement about the branch voltages being different is not correct. The total resistance in parallel is smaller than any individual branch, because multiple paths reduce overall opposition, so the statement about the total resistance being greater is false. Currents in each branch are determined by that branch’s resistance, so they’re not generally identical unless all branches have equal resistance. A quick check with numbers (for example, a 12 V source with 4 Ω and 6 Ω branches giving 3 A and 2 A) shows the total current is 5 A, the sum of the branch currents, confirming the true relationship.

In a parallel DC circuit, the current that leaves the source splits among the branches and then recombines, so the total current equals the sum of the currents in each branch. The voltage across every branch is the same as the source, which is why the statement about the branch voltages being different is not correct. The total resistance in parallel is smaller than any individual branch, because multiple paths reduce overall opposition, so the statement about the total resistance being greater is false. Currents in each branch are determined by that branch’s resistance, so they’re not generally identical unless all branches have equal resistance. A quick check with numbers (for example, a 12 V source with 4 Ω and 6 Ω branches giving 3 A and 2 A) shows the total current is 5 A, the sum of the branch currents, confirming the true relationship.