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Question

N cells each of e.m.f. E & internal resistance r are grouped into sets of K cells connected in series. The (NK) sets are connected in parallel to a load of resistance R, then:

A
Maximum power is delivered to the load if K=NRr
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B
Maximum power is delivered to the load if K=rNR
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C
Maximum power delivered to the load is NE24r
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D
Maximum power delivered to the load is E24Nr
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Solution

The correct option is C Maximum power delivered to the load is NE24r
Given that N cells are grouped into sets of K cells connected in series, So total NK rows each of emf KE and internal resistance Kr, are connected in parallel

Net emf of the circuit in a parallel setup is given by
Enet=E1r1+E2r2+E3r3+.....1r1+1r2+1r3+....
Enet=KEKr×NK1Kr×NK=KE
Net internal resistance,
1Rnet=1Kr×NK=NK2r
Rnet=K2rN


From maximum power transfer theorem, we know that internal resistance is equal to external resistance
R=K2rN
K=NRr........(1)
Now, power delivered is
P=I2R
P=(KER+R)2×R
P=K2E24R2×R=K2E24R.......(2)
put the value of K in eq. (2)
P=NRr×E24R
P=NE24r

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