Question 1 of 270705eccefa3bacbc34ba4d47eab

When the length and cross sectional area of a replacement wire are both tripled, what will be the value of the resistance as compared to the original wire?

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Question 1 of 27070
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When the length and cross sectional area of a replacement wire are both tripled, what will be the value of the resistance as compared to the original wire?

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🔍 Key Concepts

• Relationship between resistance, length, and area of a conductor: R=ρLAR = \rho \dfrac{L}{A}R=ρAL​ • Effect of multiplying length on resistance (direct proportion) • Effect of multiplying cross-sectional area on resistance (inverse proportion)

💭 Think About

• First, imagine what happens to resistance if you ONLY triple the length but keep area the same. How does that change R? • Next, imagine what happens to resistance if you ONLY triple the cross-sectional area but keep length the same. How does that change R? • Finally, combine both effects: if both length and area change together, how do these two factors multiply to give the total change in resistance?

✅ Before You Answer

• Write the ratio RnewRold\dfrac{R_{new}}{R_{old}}Rold​Rnew​​ using R=ρLAR = \rho \dfrac{L}{A}R=ρAL​ and cancel out common terms like resistivity ρ\rhoρ. • Substitute Lnew=3LL_{new} = 3LLnew​=3L and Anew=3AA_{new} = 3AAnew​=3A and simplify carefully to see the net factor change. • Make sure you correctly handle that area is in the denominator of the resistance formula, which reverses the effect of increasing it.