In a parallel circuit, the total current Is is equal to the sum of the branch currents. Which expression shows this?

• A. Is = R1 + R2 + R3
• B. Is = V1 + V2 + V3
• C. Is = V / R
• D. Is = I1 + I2 + I3

Answer: (D)

In a parallel circuit, the currents in each branch add up to the total current flowing into the junction. Each branch carries its own current (I1, I2, I3, ...), and the total current is the sum of these branch currents: Is = I1 + I2 + I3. This directly expresses how current splits and then recombines in parallel.

The other expressions don’t capture that summing of branch currents. Adding resistances would mix different quantities (currents with resistances). Adding voltages isn’t appropriate because the voltage across each parallel branch is the same, not added. Using Is = V / R could describe the total current if R is the equivalent (or total) resistance, but it doesn’t explicitly show the current from each branch summing to the total.