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Question
A piece of wire of resistance R is cut into three equal parts. These parts are then connected in parallel. If the equivalent resistance of this parallel combination is R1, what is the value of the ratio R1 : R?
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Solution 1
The resistance of each part is `"R"/3` Ω (as resistance is proportional to the length of the wire.)
`1/"R"_1 = 3/"R" + 3/"R" + 3/"R"`
`1/"R"_1= (3 + 3 + 3)/"R"`
`1/"R"_1= 9/"R"`
∴ `"R"_1 = "R"/9`
∴ `"R"_1/"R" = 1/9`
Solution 2
The resistance of each part is `"R"/3` Ω (as resistance is proportional to the length of the wire.)
`1/"R"_1 = 3/"R" + 3/"R" + 3/"R"`
`1/"R"_1= (3 + 3 + 3)/"R"`
`1/"R"_1= 9/"R"`
∴ `1/"R"_1 = 9/"R"`
∴ `"R"/"R"_1 = 9`
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