Current Electricity 3 Question 11

10. A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number N of similar cells is now connected in series with a wire of the same material and cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time. The value of N is

(2001,2M)

(a) 4

(b) 6

(c) 8

(d) 9

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Solution:

  1. In the first case (3E)2Rt=msΔT

H=V2Rt

When length of the wire is doubled, resistance and mass both are doubled.

Therefore, in the second case,

(NE)22Rt=(2m)sΔT

Dividing Eq. (ii) by (i), we get

N218=2 or N2=36 or N=6



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