In a parallel circuit, currents in branches are true about currents relative to branch resistances?

• A. Currents are equal in all branches
• B. Currents split proportionally to the branch voltages
• C. Currents split inversely with the branch resistance; higher resistance draws less current
• D. The current through each branch is independent of its resistance

Answer: (C)

In a parallel circuit the same supply voltage appears across every branch, so each branch’s current is determined by Ohm’s law I = V/R. Because the voltage is the same for all branches, the currents are inversely proportional to the branch resistances. That means a branch with higher resistance draws less current, and a branch with lower resistance draws more. The total current from the source is the sum of all branch currents.

So the statement that currents split inversely with branch resistance, with higher resistance drawing less current, is the correct description. Currents are not necessarily equal in all branches, nor proportional to branch voltages (the voltages are equal), and they are not independent of resistance.