When the length and cross sectional area of...

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Question 1 of 205eccefa3bacbc34ba4d47eab

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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5eccefa3bacbc34ba4d47eab

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 = \rho \dfrac{L}{A} ) • 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 ( \dfrac{R_{new}}{R_{old}} ) using ( R = \rho \dfrac{L}{A} ) and cancel out common terms like resistivity (\rho). • Substitute ( L_{new} = 3L ) and ( A_{new} = 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.

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Question 1 of 205eccefa3bacbc34ba4d47eab

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?

Back

Question 1 of 20

5eccefa3bacbc34ba4d47eab

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?

No comments yet

Be the first to share your thoughts!

If the question has a related picture, it will appear here.

🔍 Key Concepts

💭 Think About

✅ Before You Answer

👋 Hi! I'm Genie, your AI study assistant. How can I help you with this question?

Quick actions

— No credit card needed