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A uniform wire of resistance `4Omega` is bent into circle of radius `r`. As specimen of the same wire is connected along the dimeter of the circle. What is the equivalent resistance across the ends of this wire? |
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Answer» Correct Answer - `(4)/(4 + pi) Omega` Circumference of the circuit `= 2 pi r` its resistance `R = 4 Omega` resistance per unit length of the wire `= (R )/(2 pi R)` Resistance of the specimen connected along the diameter is `R_(1) = (R )/(2 pi r) xx 2 r = (R )/(pi)` The resistance of each senicircular wire `R_(2) = (R )/(2)` Equivalent resistance `R_(3)` across the specimen is `(1)/(R_(3)) = (2)/(R ) + (2)/(R ) + (pi)/(R ) + (4 + pi)/(R )` or `R_(3) = (R )/(4+ pi) = (4)/(4 + pi) Omega` |
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