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In physics, Ohm's law says that current through a wire, I, is directly proportional to voltage, V, and inversely proportional to resistance, R: [ I=V/R. ] It's also true that resistance is directly proportional to the length of the wire. We have a piece of wire. We pass 12 volts through this wire and measure 100 milliamps of current. If I cut the wire in half and pass 24 volts through it, how many milliamps of current will I measure?

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Due to Ohm's law, I is proportional to V and 1/R:

I ∝ V

I ∝ 1/R

R is proportional to the wire length L:

R ∝ L

Therefore I is also proportional to 1/L:

I ∝ 1/L

Calculate the scale factor due to increased voltage:

k₁ = 24/12 = 2

Calculate the scale factor due to decreased wire length:

k₂ = 1/(0.5/1) = 2

Multiply the original current by the scale factors to get the new current:

I = I₀k₁k₂

I₀ = 100mA, k₁ = 2, k₂ = 2

I = 100(2)(2)

I = 400mA

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