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Question-36700




Question Number 36700 by rahul 19 last updated on 04/Jun/18
Answered by tanmay.chaudhury50@gmail.com last updated on 04/Jun/18
R_2 andR_x  parralal so equivalant resistance  =((30x)/(30+x))  total resistance=R=20+((30x)/(30+x))  =((600+50x)/(30+x))  thermal power=(V^2 /R)  p=((V^2 ×(30+x))/(600+50x))  now xchanges to x+△x  p changes to p+△p  to show when △x→0  △p→0  p+△p=V^2 ×(((30+x+△x))/(600+50x+50△x))  △p=V^2 ×{((30+x+△x)/(600+50x+50△x))−((30+x)/(600+50x))}  =V^2 {((18000+1500x+600x+50x^2 +△x(600+50x))/)   ((−18000−1500x−1500△x−600x−50x^2 −x50△x)/)  =(N_r /D_r )  when △x→0  the value of N_r →0  that means △p→0  hence proved
R2andRxparralalsoequivalantresistance=30x30+xtotalresistance=R=20+30x30+x=600+50x30+xthermalpower=V2Rp=V2×(30+x)600+50xnowxchangestox+xpchangestop+ptoshowwhenx0p0p+p=V2×(30+x+x)600+50x+50xp=V2×{30+x+x600+50x+50x30+x600+50x}=V2{18000+1500x+600x+50x2+x(600+50x)180001500x1500x600x50x2x50x=NrDrwhenx0thevalueofNr0thatmeansp0henceproved
Commented by rahul 19 last updated on 04/Jun/18
So, what is the final value of R_x  ??
So,whatisthefinalvalueofRx??
Commented by tanmay.chaudhury50@gmail.com last updated on 04/Jun/18
data insufficient..because p=(v^2 /R)  to find we need v and p
datainsufficient..becausep=v2Rtofindweneedvandp
Answered by ajfour last updated on 15/Jun/18
let R_x =x  P_x =i_x ^2 x  P_x = [(V^(  2) /((20+((30x)/(30+x)))^2 ))×(((30)/(30+x)))^2 ]x     =((900V^(  2) x)/((1800+50x)^2 )) = ((9V^(  2) )/(25))×(x/((x+36)^2 ))  for small variations in x  if power doesn′t change much  then for such a value of x  (dP_x /dx)=0 ; ⇒ (x+36)^2 =2x(x+36)  ⇒     x = 18 Ω .
letRx=xPx=ix2xPx=[V2(20+30x30+x)2×(3030+x)2]x=900V2x(1800+50x)2=9V225×x(x+36)2forsmallvariationsinxifpowerdoesntchangemuchthenforsuchavalueofxdPxdx=0;(x+36)2=2x(x+36)x=18Ω.

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