The voltage of a generator is 220V. If approximately 8V are lost in a supply line, what is the rate of voltage lost?
Answer (2)
The rate of voltage lost from a generator with an original voltage of 220V, given an 8V loss, is approximately 3.64%. This is calculated by dividing the lost voltage by the original voltage and converting the result to a percentage. Understanding this loss is important for efficiency in power systems.
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Calculate the rate of voltage loss: r a t e = 220 8 .
Convert the rate to a percentage: p erce n t a g e _ l oss = r a t e × 100 .
Calculate the percentage loss: p erce n t a g e _ l oss = 220 8 × 100 = 3.63636... .
Round the result to two decimal places: The rate of voltage lost is approximately 3.64% .
Explanation
Understanding the Problem We are given that the voltage of a generator is 220V and that approximately 8V are lost in the supply line. We need to find the rate of voltage lost, expressed as a percentage.
Calculating the Rate of Voltage Loss To find the rate of voltage loss, we will divide the voltage lost by the original voltage. This will give us the rate as a decimal.
Setting up the Calculation The rate of voltage loss is calculated as follows: r a t e = or i g ina l _ v o lt a g e v o lt a g e _ l os t = 220 8
Calculating the Rate Now, we calculate the rate: r a t e = 220 8 = 0.0363636...
Converting to Percentage To express this rate as a percentage, we multiply by 100: p erce n t a g e _ l oss = r a t e × 100 = 0.0363636... × 100 = 3.63636...
Rounding the Result Rounding this to two decimal places, we get 3.64%.
Final Answer Therefore, the rate of voltage lost is approximately 3.64%.
Examples
Understanding percentage loss is crucial in many real-world applications. For example, when investing, knowing the percentage loss on an investment helps assess risk. Similarly, in retail, calculating the percentage markdown on a product helps determine its sale price. In electrical engineering, like in this problem, it helps to quantify energy losses in transmission lines, which is essential for improving efficiency and reducing waste. This concept is also used in quality control to measure the percentage of defective items in a production batch, ensuring standards are met.
