Five cells have been connected in parallel to form a battery. The emf and intenal resistances of the cells have been shown in figure. If a load resistance R is connected to the battery, then
A
Current passing through the cell is maximum which has smallest value of internal resistance.
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B
Current passing through the cell is maximum which has largest value of internal resistance.
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C
Internal resistance of equivalent cell is larger than the internal resistance of any cell connected.
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D
Equivalent emf is 80E31
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Solution
The correct option is D Equivalent emf is 80E31 The internal resistance of equivalent cell is given by
1r0=1r+12r+..........+116r
⇒1r0=1r[11+12+.....+124]
Using , Sn=a(1−rn)(1−r)
1r0=1r×1×[1−(12)5][1−12]
⇒1r0=3116r
Clearly, r0 is smaller than any value of internal resistance of cells connected in the circuit.
So, option (c) is wrong.
If we write the voltage equation for a loop containing any cell (nth cell) and load resistance R , we get
inrn=En−IR
⇒in=Enrn−IRrn
From the diagram, it is clear that the value of Enrn=Er for all the cells.
∴in=Er−IRrn
Thus, in is maximum for the cell which has largest value of rn.
So, option (a) is wrong and option (b) is correct.
Equivalent enf E0=Er+2E2r+4E4r+8E8r+16E16r1r0
=5Er×16r31=80E31
Hence, options (b) and (d) are the correct alternatives to the given question.