Power in parallel — additivity: For independent branches connected in parallel to the same voltage source, does the total power drawn from the source equal the arithmetic sum of the individual branch powers?

Introduction / Context:
Total power accounting is a basic check for energy balance in circuits. In parallel networks, each branch sees the same voltage, and the source must supply the sum of branch powers under steady operation. This principle is used in sizing supplies and estimating thermal loads.

Given Data / Assumptions:

• Parallel branches under a common source voltage.
• Independent loads; coupling between branches is negligible.
• Ideal measurement and wiring assumed for the concept.

Concept / Approach:
Branch power P_k = V * I_k (resistive DC) or P_k = V_rms * I_rms * pf_k (AC). The source current is I_total = sum(I_k). Therefore total power P_total = V * sum(I_k) in DC, which equals sum(V * I_k) = sum(P_k). In AC with sinusoidal steady state, active power is still additive across independent branches when using correct rms values and power factors.

Step-by-Step Solution:

Verification / Alternative check:
Bench tests with two resistors in parallel show power meter at the source equals the sum of two individual power readings, within instrument tolerance. Power conservation ensures additivity for independent branches.

Why Other Options Are Wrong:

• Incorrect: Conflicts with energy conservation in independent parallel branches.
• Only true for DC resistive loads: Also true for AC active power with proper power factor accounting.
• Only true when impedances are equal: Equality is not required for additivity.
• Only true when voltage is below 10 V: Magnitude is irrelevant to the principle.

Common Pitfalls:
Confusing instantaneous power oscillations with average power; forgetting power factor in AC and then misinterpreting measurements.

Final Answer:
Correct