Electromagnetic Induction and Alternating Current 4 Question 18

####18. In the circuit shown A and B are two cells of same emf E but different internal resistances r1 and r2(r1>r2) respectively. Find the value of R such that the potential difference across the terminals of cell A is zero, a long time after the key K is closed.

(2004,4M)

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Answer:

Correct Answer: 18. R=43(r1r2)

Solution:

  1. After a long time, resistance across an inductor becomes zero while resistance across capacitor becomes infinite. Hence, net external resistance,

Rnet=R2+R2=3R4

Current through the batteries, i=2E3R4+r1+r2

Given that potential across the terminals of cell A is zero.

Eir1=0 or E2E3R/4+r1+r2r1=0

Solving this equation, we get, R=43(r1r2)



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