A wire of length L and 3 identical cells of negligible internal resistance are connected in series. Due to the current, the temperature of the wire is raised by `DeltaT` 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 `DeltaT` in the same time t. the value of N is

Options

A. 4
B. 6
C. 8
D. 9

Answer

B

Explanation

Let the resistor to be connected across CD be x. Then the equivalent resistance across EF should be x and also across AB should be x. So we get
`((2R +x )R)/(3R +x) = x`.

Solve to get `x = (sqrt 3 -1 )R`