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The current in a circuit varies inversely as the resistance. The current is 21 Amperes, when the...

Question:

The current in a circuit varies inversely as the resistance. The current is 21 Amperes, when the resistance is 5 ohms. Find the current for existence of 20 Ohms.

Proportions and Variation:

When we have a numerical ratio, it indicates the relationship between two numbers {eq}a {/eq} and {eq}b {/eq}. On the other hand, a proportion indicates the similarity between two ratios. When two variables are interdependent, changes in the value of one variable will have a proportional effect on the other. Variations occur when there is an increase or decrease of a variable {eq}a {/eq} with respect to another {eq}b {/eq}, for a ratio or constant {eq}k {/eq}. In the circumstance that we have an inverse variation, it occurs that when one variable decreases the other increases, which we can also write as {eq}a = \dfrac{k}{b}{\text{,}}\,{\text{ or }}\,k = a \cdot b {/eq}.

Answer and Explanation:

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Given Data:

  • Current {eq}1{/eq}, {eq}(I_1) = 21\ \rm A {/eq}
  • Resistance {eq}1{/eq}, {eq}(R_1) = 5\ \Omega {/eq}
  • Resistance {eq}2{/eq}, {eq}(R_2) =...

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