Parallel RC branch currents: A parallel RC circuit has 100 mA through the resistive branch and 100 mA through the capacitive branch (rms). What is the total rms source current?

Introduction / Context:
In parallel RC circuits, the resistive branch current is in phase with the voltage, while the capacitive branch current leads the voltage by 90°. Because these branch currents are orthogonal phasors, the total rms current is found using the Pythagorean sum, not simple arithmetic addition.

Given Data / Assumptions:

• I_R = 100 mA (in phase with V).
• I_C = 100 mA (leads V by 90°).
• Sinusoidal steady state; branch currents are orthogonal.

Concept / Approach:

Total current magnitude I_T = √(I_R^2 + I_C^2) because the phasors are at right angles. This is analogous to vector addition of perpendicular components on the complex plane.

Step-by-Step Solution:

Verification / Alternative check:

Phasor diagram confirms orthogonality; if the two were in phase, the total would be 200 mA, but here orthogonal components yield 141 mA.

Why Other Options Are Wrong:

200 mA assumes in-phase addition. 100 mA ignores the other branch. 282 mA wrongly doubles the Pythagorean result.

Common Pitfalls:

Adding magnitudes linearly; forgetting phase relationships in reactive branches.

Final Answer:

141 mA