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Question

Chemistry Question on types of cells

Two cells each of same emf e but of internal resistances r1r_1 and r2r_2 are connected in series through an external resistance R. If the potential difference between the ends of the first cell is zero, what will be the value of R in terms of r1r_1 and r2r_2 ?

A

r1r2r_1 - r_2

B

r1+r2r_1 + r_2

C

2r1r22r_1 - r_2

D

2r1+r22r_1 + r_2

Answer

r1r2r_1 - r_2

Explanation

Solution

Current in the circuit I=2e(r1+r2)+RI = \frac{2e}{(r_1 + r_2) + R } and eIr1=0e - Ir_1 = 0 e2er1(r1+r2)+R=0\Rightarrow e - \frac{2er_1}{(r_1 + r_2) + R } = 0 er2er1+eR(r1+r2)+R=0\Rightarrow \frac{er_2 - er_1 + eR}{(r_1 + r_2) + R }= 0 r2r1+R=0\Rightarrow r_2 - r_1 + R = 0 or R=(r1r2)R = (r_1 - r_2)