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If a wire of resistance R, resistivity ñ "roe", length L, and cross sectional area A, had its length doubled and radius halved, what would be the ratio of R'/R. Where R' is the new resistance of the wire.

I thought it would be 4 times R, giving the ratio of 4R:R'
However, I plugged theoretical numbers in to check and it did not match what I thought. Can someone please explain the ratio to me?

  • Physics -

    R2= ρ•L2/A2= ρ•2•L1•2/A1=4• ρ•L1/A1=4•R1

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