Which of the four resistances will generate the greatest amount of heat when current flows from X to Y in the network shown here(see image)? a)P= 2ohm b)Q= 4ohm c)R= 1ohm d)S= 2ohm please give reason.

Asked by sumandeesinghrana | 12th Oct, 2010, 08:50: PM

Expert Answer:

In series system ,resistance with larger value generates more heat compared to lower resistance,because current is same in both resistance and heat = i2 R.
In parallel system resistance with lower value genrates more heat compared to higher resistance,because potential across both resistance is same and heat=V2/R.
So, In the given problem
more heat will be generated in lower branch with R & S ;compared to upper branch with P & Q ; because (R+S)<(P+Q) : (parallel system).

In lower branch more heat will be generated in S compared to R , since S>R (series system)
 
Therefore S will generate greatest amount of heat.
 
Better Method:
Let current through point X (or Y) is i.
   Resistance between X and Y  R =
therefore potential difference between X and Y is
Vxy = 20*i
Let current through branch P & Q is i1 and through branch R & S is i2 .
then
i1 *(P+Q)= Vxy
             = 20*i  
and
i2 *(R+S)=Vxy
             = 20*i
on solving we get
 i1 = i/3
 i2 =2i/3     (Note that i1 +i2 = i : total current)
 
Now heat generated by S and Q is
 
Clearly   HS > HQ

Answered by  | 13th Oct, 2010, 11:26: AM

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