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Given equation : I=E/(R₁+r)

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Multiply each side by (R₁+r).

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I(R₁+r)=E

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Divide each side by I.

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(R₁+r)=E/I

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Subtract R₁ from each side.

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r=(E/I)-R₁

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The solution is r=(E/I)-R₁

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