Current Electricity and Electrical InstrumentHard

Question

Under what condition current passing through the resistance R can be increased by short circuiting the battery of emf E2. The internal resistances of the two batteries are r1 and r2 respectively. 

Options

A.E2r1 > E1(R + r2)
B.E1r2 > E2(R + r1)
C.E2r2 > E1(R + r2)
D.E1r1 > E2(R + r1)

Solution

(E1 + E2)(r1 + R) < E1 (r1 + r2 + R)
E1R + E2R + E1R < E1r2 + E1R; R(E1 + E2) < E1r2
On solving we get E1r2 > E2 (R + r1)

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