What is the relationship between efficiency and operating costs?

Question

Examoogle · Accepted Answer

Option C: efficiency is Inverse proportion to the operating costs

Explanation & Concepts:
Efficiency is defined as the ratio of output power to input power. As operating costs—which primarily consist of input energy consumption—increase for a fixed output, the efficiency of the machine decreases, establishing an inverse relationship.

Working Principle: The efficiency (\eta) of an electrical machine is given by the ratio of output power (P_{out}) to the sum of output power and losses (P_{loss}). Operating costs are directly proportional to the total input power (P_{in} = P_{out} + P_{loss}). Therefore, as costs increase due to higher losses, the efficiency drops.

Key Formulas: $\eta = \frac{P_{out}}{P_{out} + P_{loss}}$ — Efficiency formula; $Cost \propto P_{in} = P_{out} + P_{loss}$ — Relationship between cost and input power

Key Points: Efficiency signifies how well an electrical machine converts input energy to useful work.; Operating costs increase if losses increase or if the machine runs at low power factor.; Higher efficiency implies lower input energy consumption for the same output.; For Induction Motors, the slip (s) directly affects the efficiency.

Advantages: Maximizes energy utilization; Reduces thermal stress on machine insulation

Disadvantages: High initial cost for high-efficiency motors; Complex design requirements for heat dissipation

Applications: Industrial motor drives; Energy-efficient pump systems

Additional Info: An inverse proportion means as one value increases, the other decreases. Here, high operating costs indicate high losses relative to output.. Option B is incorrect because direct proportion would imply that more expensive machines are always more efficient, which is a fallacy.

Answer: C is correct — Efficiency is inversely proportional to the operating costs because higher costs for a given output indicate higher input requirements and/or increased internal losses.

Exam Tip: In competitive exams, always link efficiency to losses; remember that any increase in operational losses will inherently drive down efficiency and increase costs.

Examoogle · Answer

Option A: efficiency is directly proportional to the square of the operating cost

Examoogle · Answer

Option B: efficiency is directly proportional to the operating costs

Examoogle · Answer

Option D: efficiency is Inverse proportion to the square of the operating costs

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)