Power factor and losses: In an RL circuit, which power factor value yields the least energy loss for a given delivered power?

Introduction / Context:
Power factor (PF) quantifies the ratio of real power to apparent power. A higher PF means less reactive current and typically lower I^2R losses in conductors and equipment for the same delivered real power, improving efficiency.

Given Data / Assumptions:

• Comparing several PF values: 1, 0.8, 0.4, 0.2.
• Same delivered real power is assumed for a fair comparison of losses.

Concept / Approach:
For fixed real power P, the apparent power S = P / PF. Current I ∝ S (for a given voltage). Lower PF means larger S and larger current, which increases copper losses proportional to I^2. Thus, maximum PF (unity) minimizes losses.

Step-by-Step Reasoning:
S = P / PFI ∝ S ⇒ I ∝ 1 / PFLoss ∝ I^2 ⇒ Loss ∝ 1 / PF^2Highest PF (1) ⇒ smallest current ⇒ least I^2R loss

Verification / Alternative check:
Example: For P = 1 kW at 100 V line, PF = 1 ⇒ S = 1 kVA ⇒ I = 10 A. At PF = 0.5 ⇒ S = 2 kVA ⇒ I = 20 A ⇒ losses are quadrupled for the same P. Hence PF = 1 minimizes losses.

Why Other Options Are Wrong:

• 0.8, 0.4, 0.2: Each progressively increases apparent power and current, causing higher losses.

Common Pitfalls:
Confusing reactive power correction with real power savings; PF correction reduces losses and capacity requirements even if delivered P is unchanged.

Final Answer:
1