7.3 Efficiency Calculations

## Introduction Every electrical system loses some energy as heat. Even a simple resistor divider wastes part of the power supplied to it. When technicians look at how much useful power a circuit delivers compared to how much it consumes, they are working with **efficiency**. In the field, this idea comes up often: power supplies, converters, lighting circuits, and test equipment all have efficiency values that affect performance and heat levels. Understanding efficiency calculations helps you make informed choices, reduce wasted energy, and troubleshoot systems that run hotter than expected. ## Key Concept Efficiency describes how effectively a circuit or component converts input power into useful output power. It is written as a percentage. The basic formula is: $\text{Efficiency}=\frac{P_{out}}{P_{in}}\times100\%$ Where: * $P_{out}$ is the useful power delivered to the load * $P_{in}$ is the total power consumed from the source In a purely resistive system, wasted power usually appears as heat. Any difference between input and output power represents energy lost inside the circuit. > [!info] Simple Definition > Efficiency tells you how much of the power you pay for actually does useful work. ## How It Works Efficiency calculations are straightforward when you break the circuit into input power and output power. A few ideas help clarify the process: 1. **All circuits have losses** Even basic wiring has resistance, which causes some power to be lost as heat. No real system is 100 percent efficient. 2. **Identify the useful output** In a heating element, the heat itself is the useful output. In a motor, the useful output is mechanical rotation. For a resistor used only for dropping voltage, nearly all the input power is waste. 3. **Difference between input and output equals loss** If a system takes in 100 W and delivers 70 W to the load, then 30 W is lost as heat somewhere in the circuit. 4. **Efficiency affects temperature rise** Lower efficiency means more heat. More heat means larger components, better cooling, or shorter equipment life. > [!tip] Quick Check > If a circuit runs much hotter than expected, check efficiency. High internal losses are a common cause. ## Real-World Application A technician evaluates a small DC power supply that delivers 12 V at 1 A to a load. The input draw from the mains is measured at 18 W. Output power: $P_{out}=12\text{ V}\times1\text{ A}=12\text{ W}$ Efficiency: $\text{Efficiency}=\frac{12}{18}\times100\%=67\%$ This means 33 percent of the input power becomes heat inside the supply. If the power supply sits in a warm panel, this heat buildup could push temperatures near the unit’s design limits. In another situation, a panel uses a resistor to drop voltage from 24 V to 12 V for an indicator that requires 0.1 A. The resistor dissipates: $P_{loss}=I^{2}R=(0.1\text{ A})^{2}\times120\Omega=1.2\text{ W}$ The indicator uses only: $P_{out}=12\text{ V}\times0.1\text{ A}=1.2\text{ W}$ Total input power: $P_{in}=P_{out}+P_{loss}=2.4\text{ W}$ Efficiency: $\frac{1.2}{2.4}\times100\%=50\%$ Only half of the power delivered into this part of the circuit is useful. This explains why the resistor runs hot and why such setups are avoided in modern control systems when a regulator or DC-DC converter can perform the same job with much higher efficiency. > [!note] Field Insight > Linear circuits like resistors and linear regulators often have low efficiency. Switching converters and LED drivers are far more efficient. ## Safety Notes Efficiency problems often lead to excess heat, which creates hazards in electrical environments. * **Overheating Components** Equipment with low efficiency runs warm. Poor ventilation or high ambient temperatures increase the risk of thermal damage. * **Fire and Breakdown** Losses accumulate as heat inside wiring, resistors, or devices. OSHA 1910.303 requires components to be used within their ratings, which includes proper thermal conditions. * **Energy Waste in Load Testing** During load bank operations, efficiency loss becomes heat that must be dissipated. Ensure that high-power resistors and load banks are placed in well-ventilated areas. * **Reduced Lifespan** High internal losses stress components. NFPA 70E encourages maintaining equipment in a condition that supports safe operation, which includes keeping temperatures under control. > [!warning] Always confirm cooling paths > Blocked airflow or crowded panels amplify the effects of low efficiency. ## Summary Efficiency calculations compare useful output power to total input power. They help explain why circuits get hot, how much energy is wasted, and whether a component or system is operating properly. By using the formula $\frac{P_{out}}{P_{in}}\times100\%$, technicians can quickly evaluate performance and identify loss points. In practice, efficiency influences equipment selection, panel layout, cooling arrangements, and troubleshooting decisions. Understanding efficiency is essential when working with power supplies, resistive loads, and real-world electrical systems. > [!columns] > >[!info] Previous lesson > ⬅️ [[7.2 Power Dissipation]] > > >[!info] Next lesson > ➡️ [[7.4 Energy Consumption (Wh and kWh)]]