Question : A wire of resistance R is cut into 'n' equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be
Option 1: nR
Option 2: R/n
Option 3: n/R
Option 4: R/n2
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Correct Answer: R/n
Solution : The correct option is R/n .
The equivalent resistance of the combination may be determined using the formula:
1/R = (1/R₁) + (1/R₂) + (1/R₃) + ... + (1/Rₙ)
In this case, all the 'n' equal parts of the wire have the same resistance, which is R. Therefore, for 'n' parts connected in parallel, you can simplify the formula as follows:
1/R = n/R
Now, solve for R_eq:
R = R/n
So, the equivalent resistance of 'n' equal parts of the wire connected in parallel is R/n.
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