Question
Mon February 20, 2012 By:
 

A current of 10A is required to flow through a resistor of 3ohm. Find the minimum no. of cells to be used of emf 10V and internal resistance as 1ohm to accomplish this. Also find the dissipated power.

Expert Reply
Wed April 11, 2012
Let us suppose that m parallel cells rows are formed, with each row having n cells in series.
Total emf in this case would be, E=nV, where V is the emf of a single cell.
total internal resistance would be nr/m.
Hence total resistance of the circuit will be R+nr/m
So, current would be given by
 
I=nV/(R+nr/m) = mnV/(nr+mR)
 
Now , in the given question, V=10, I=10, R=3 and r=1ohm
So, putting the values, we get
 
10=mn10/(n+m3)
or, 3m+n=mn
 
For minimum values of m and n to satisfy this equation would be m=2 and n=6
So, minimum number of cells becomes 2x6=12 cells.
 
Power dissipated in this case,
I=120/6+6 = 10
Resistance eq.=3+6/2 = 6
P=I2Req= 100x6=600W
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