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Multiple choice physics electrical circuits domestic electric circuits and safety precautions domestic and commercial circuit electric power

A certain network consists of two ideal and indentical voltage sources in series and a large number of ideal resistor. The power consumed in one of the resistor is $4W$ when either of the two sources is active and other is replaced by a short circuit. The power consumed by same resistor when both sources are simultaneously active would be: 

  1. $0$ or $16W$

  2. $4W$ or $8W$

  3. $0$ or $8W$

  4. $8W$ or $16W$
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A Correct answer
Explanation

$ P=VI$

$ I= \cfrac{nE}{R+r}$ (r=0)
In this case 
$ I= \cfrac{nE}{NR} ; E _1 = E _2$
$ P=VI$
In first case 
$ 4 =E \times \cfrac{E}{NR} = \cfrac{E^2}{NR}$
In second case 
$ x =2E \times \cfrac{2E}{NR} = \cfrac{4E^2}{NR}$
$ \cfrac{x}{4} = \cfrac{4E^2}{NR} \times \cfrac{NR}{E^2}$
$ x= 0 \quad or \quad 16W$