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Question
A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then the ratio `"R"/"R'"` is ______.
Options
`1/25`
`1/5`
5
25
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Solution
A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R’, then the ratio `"R"/"R'"` is 25.
Explanation:
The resistance is cut into five equal parts, which means that the resistance of each part is `"R"/5`.
We know that each part is connected to each other in parallel, hence the equivalent resistance can be calculated as follows:
`1/"R'" = 5/"R" + 5/"R" + 5/"R" + 5/"R" + 5/"R"`
= `(5 + 5 + 5 + 5 + 5)/"R"`
= `25/"R"`
`"R"/"R'"` = 25
The ratio of `"R"/"R'"` is 25.
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