QuestionApril 29, 2025

Conductor power losses are directly proportional to the length of the conductor and the square of the current. If the current is doubled, the power loss will be increased by __ percent. 100 200 300 400

Conductor power losses are directly proportional to the length of the conductor and the square of the current. If the current is doubled, the power loss will be increased by __ percent. 100 200 300 400
Conductor power losses are directly proportional to the length of the conductor and the square of the current. If the current is doubled, the power loss will be increased by __ percent. 100 200 300 400

Solution
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Answer

300 Explanation 1. Write the relationship for power loss Power loss P \propto I^2, where I is the current. 2. Analyze the effect of doubling the current If I is doubled, new current I' = 2I. Substituting into the formula: P' \propto (2I)^2 = 4I^2. This means the new power loss is 4 times the original. 3. Calculate the percentage increase Percentage increase = \frac{P' - P}{P} \times 100 = \frac{4P - P}{P} \times 100 = 300\%.

Explanation

1. Write the relationship for power loss<br /> Power loss $P \propto I^2$, where $I$ is the current.<br /><br />2. Analyze the effect of doubling the current<br /> If $I$ is doubled, new current $I' = 2I$. Substituting into the formula:<br />$P' \propto (2I)^2 = 4I^2$. This means the new power loss is 4 times the original.<br /><br />3. Calculate the percentage increase<br /> Percentage increase = $\frac{P' - P}{P} \times 100 = \frac{4P - P}{P} \times 100 = 300\%$.
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