A wire is being used as a replacement having twice the length and one-half the cross-sectional area of the original wire. What will be the resistance of this new wire, when compared to that of the original wire?
• Relationship between resistance (R), length (L), and cross‑sectional area (A) of a conductor • How changing length affects resistance if all other factors stay the same • How changing area affects resistance if all other factors stay the same
• Write the basic formula that shows how resistance depends on length and area, then think: if you double the length, what happens to R? • Using the same formula, if you cut the cross‑sectional area in half, what happens to R? • Combine both effects: start with the original resistance as 1R, then apply the length change and area change step by step to see the final multiple of R.
• Be sure your formula has length (L) in the numerator and area (A) in the denominator • Treat the original resistance as R = 1 and express the new resistance as a multiple of R • Carefully multiply the two change factors (from length and from area) together before picking an answer
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