Which statement about parallel circuits is not true?

• A. The same voltage is across each branch.
• B. The total current equals the sum of branch currents.
• C. The total resistance is greater than the smallest branch resistance.
• D. The current through a branch is proportional to its resistance.

Answer: (D)

In a parallel circuit, the same voltage is across every branch, and each branch draws current according to I = V/R. Since the voltage is the same for all branches, the current in each branch depends on 1/R, meaning it is inversely proportional to the branch’s resistance. The statement that the current through a branch is proportional to its resistance is not true. For example, with the same supply voltage, a smaller resistance branch draws more current, while a larger resistance branch draws less, in inverse relation to their resistances. The total current is the sum of all branch currents, and the equivalent (total) resistance of parallel branches is less than the smallest individual branch resistance.