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Two wires A and B of same material and mass have their lengths in the ratio 1 : 2. On connecting them to the same source, the rate of heat dissipation in B is found to be 5 W. The rate of heat dissipation in A is

a
10 W
b
5 W
c
20 W
d
none of these

detailed solution

Correct option is C

Ht =P = V2R ⇒  P  ∝  1R ;  Also R ∝ lA∝ l2ρA.lρ⇒  R  ∝  l2m  ⇒  R ∝  l2 for  same massSo  PAPB =  lB2lA2 =  41  ⇒  PA =20  W

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