Which statement is correct about a parallel circuit?

Which statement is correct about a parallel circuit?

• A. The current is equal in all portions of the circuit
• B. The branch currents are equal to the total current
• C. The total current is equal to the sum of the currents through the individual branches of the circuit
• D. The total resistance is equal to the sum of the branch resistances

Answer: (C)

In a parallel circuit, the same voltage is across every branch, and the current from the source splits among those branches. The total current drawn from the supply is the sum of the currents through each branch, because the currents combine at the junctions as they flow through the parallel network. This is why the correct statement is that the total current equals the sum of the currents in the individual branches. Remember that branch currents depend on each branch’s resistance via I = V/R, so the currents in different branches are not necessarily equal unless the resistances are identical. Also, the total current is not simply the current in any one branch, nor is the total resistance the sum of the branch resistances; in parallel, the total resistance is found from the reciprocal relationship 1/R_total = sum(1/R_i).

In a parallel circuit, the same voltage is across every branch, and the current from the source splits among those branches. The total current drawn from the supply is the sum of the currents through each branch, because the currents combine at the junctions as they flow through the parallel network. This is why the correct statement is that the total current equals the sum of the currents in the individual branches.

Remember that branch currents depend on each branch’s resistance via I = V/R, so the currents in different branches are not necessarily equal unless the resistances are identical. Also, the total current is not simply the current in any one branch, nor is the total resistance the sum of the branch resistances; in parallel, the total resistance is found from the reciprocal relationship 1/R_total = sum(1/R_i).