Question

Two cells each of same emf e but of internal resistances $ r_1 $ and $ r_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 $ r_1 $ and $ r_2 $ ?

• A. $ r_1 - r_2 $
• B. $ r_1 + r_2 $
• C. $ 2r_1 - r_2 $
• D. $2r_1 + r_2 $

Answer 1

The Correct Option is A

Current in the circuit $ I = \frac{2e}{(r_1 + r_2) + R } $ and $ e - Ir_1 = 0 $ $ \Rightarrow e - \frac{2er_1}{(r_1 + r_2) + R } = 0 $ $ \Rightarrow \frac{er_2 - er_1 + eR}{(r_1 + r_2) + R }= 0 $ $ \Rightarrow r_2 - r_1 + R = 0 $ or $ R = (r_1 - r_2) $