A piece of wire of resistance R is cut into five equal parts. These parts are thenconnected in parallel. If the equivalent resistance of this combination is R′, then theratio R/R′ is –
Question
A piece of wire of resistance R is cut into five equal parts. These parts are thenconnected in parallel. If the equivalent resistance of this combination is R′, then theratio R/R′ is –
Solution
The resistance of a wire is directly proportional to its length. So, if the wire is cut into 5 equal parts, the resistance of each part will be R/5.
When resistors are connected in parallel, the total or equivalent resistance (R') can be found using the formula 1/R' = 1/R1 + 1/R2 + 1/R3 + ...
In this case, all the resistances are equal (R/5), so the formula becomes 1/R' = 5/(R/5).
Solving this gives R' = R/25.
Therefore, the ratio R/R' = R/(R/25) = 25.
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