Compared to the original wire, what will be the resistance of a replacement wire having twice the length and one-half the cross-sectional area of the original?
• Resistance formula for a conductor in terms of length and cross‑sectional area • How changing length affects resistance when all else is constant • How changing area affects resistance when all else is constant
• Write the relationship between resistance, length, and area, then treat each change (length and area) one at a time to see its effect • Think in terms of multipliers: how many times larger or smaller does the resistance become from each change, then combine those multipliers • Ask yourself whether making a wire longer and thinner makes it easier or harder for current to flow
• Verify that resistance is directly proportional to length • Verify that resistance is inversely proportional to cross‑sectional area • After applying both changes, multiply the effects to see the overall factor change in resistance before picking a choice
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