Which statement about parallel circuits is false?

Which statement about parallel circuits is false?

• A. The voltage across each branch is the same as the source
• B. The current in each branch is independent of the others
• C. The total resistance in parallel is the sum of branch resistances
• D. The currents in all branches are equal

Answer: (D)

In a parallel circuit, all branches are connected to the same two points, so the voltage across each branch is the same as the source. That means each branch sees the full supply voltage, regardless of how many other branches exist. Currents in the branches behave according to each branch’s resistance. With the same voltage, a branch with lower resistance draws more current than a branch with higher resistance. Because the currents depend on the individual resistances, they do not have to be equal. They will be equal only if every branch has identical resistance. The total or equivalent resistance of a parallel network is not the sum of the branch resistances. Instead, you add the reciprocals of the branch resistances and take the reciprocal of that sum (1/Rtotal = 1/R1 + 1/R2 + ...). This makes the parallel combination have a smaller total resistance than any single branch. So the statement that currents in all branches are equal is not generally true; it only holds when all branch resistances are the same.

In a parallel circuit, all branches are connected to the same two points, so the voltage across each branch is the same as the source. That means each branch sees the full supply voltage, regardless of how many other branches exist.

Currents in the branches behave according to each branch’s resistance. With the same voltage, a branch with lower resistance draws more current than a branch with higher resistance. Because the currents depend on the individual resistances, they do not have to be equal. They will be equal only if every branch has identical resistance.

The total or equivalent resistance of a parallel network is not the sum of the branch resistances. Instead, you add the reciprocals of the branch resistances and take the reciprocal of that sum (1/Rtotal = 1/R1 + 1/R2 + ...). This makes the parallel combination have a smaller total resistance than any single branch.

So the statement that currents in all branches are equal is not generally true; it only holds when all branch resistances are the same.