Question -
A uniform wire of resistance 4 ohm is bent into the form of a circle of radius r. A specimen of the same wire is connected along the diameter of the circle. What is the equivalent resistance across the ends of this wire?
Options:
A .  44+π ohm
B .  33+π ohm
C .  22+π ohm
D .  11+π ohm
Answer: Option A : A Circumference of the circle = 2πr Therefore the resistance per unit length of the wire = R2πr where r= 4 ohm is the resistance of wire Now the length of the specimen connected along the diameter = 2r Therefore the resistance of this specimen is R1=R2πr×2r=Rπ also the resistance of each semicircle is R2=R2 equivalent resistance R' across the specimen is given by 1R′=2R+2R+πR=4+πR R′=R4+π=44+π ohm
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