A Copper wire has a resistance of 0.5 ohm.Another copper wire of the same mass as the first one is double in length of the first.Find the resistance of the second wire.

Asked by Jai Gupta | 17th May, 2013, 09:47: AM

Expert Answer:

Mass of the copper wire is same. 
M1 = M2
d*pi*r1^2*l1 = d*pi*r2^2*l2 (where d is the density of copper, r1 and r2 are the radius of 2 wires, l1 and l2 is their lengths)
 
Now, l2 = 2l1
Hence, d*pi*r1^2*l1 = d*pi*r2^2*2l1
 r1^2 = 2r2^2
r2^2 = r1^2/2
 
For first wire, Resistance = rho*l1/A1
0.5 = rho*l1/pi*r1^2 
 
For second wire, resistance =  rho*l2/A2
= rho*l2/pi*r2^2 
= rho*2l1/pi(r1^2/2)
= 4( rho*l1/pi*r1^2 )
= 4*0.5
= 2 ohm

Answered by  | 18th May, 2013, 12:29: AM

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