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The internal resistance of two identical cells, with same current whether joined in series or parallel to a 1Ω resistor is​
  • a)
    1 ohm
  • b)
    0.5 ohm
  • c)
    1.5 ohm
  • d)
    2 ohm
Correct answer is 'A'. Can you explain this answer?
Verified Answer
The internal resistance of two identical cells, with same current whet...
1st case[series]
I=E+E/r+r+1-----1
2nd case[parallel]
I=E[E will be same in parallel]/(1/r)+(1/r)+(1/1)----2
Current in both cases are the same.
1=2
2E/2r+1=E/(2/r)+1
R=1 Ω
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Most Upvoted Answer
The internal resistance of two identical cells, with same current whet...
let the resistance of the two cells be 'r'

now,

when joined in series

RS = r + r + 1 

or

RS = 2r + 1

the series current in this case would be

IS= V/R = 2E/RS

[V = E + E - total emf]

or

IS = 2E / (2r + 1)

and

when joined in parallel

1/RP = (1/r) + (1/r) + 1

or

RP = 1 + r/2

the parallel current in this case would be

IP = V/RP = E/RP

or

IP = E / (1 + r/2)

now,

we are given 

IS = IP

so,

 2E / (2r + 1) = E / (1 + r/2)

or

2 + r = 2r + 1

thus,

r = 1 ohm
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The internal resistance of two identical cells, with same current whet...
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The internal resistance of two identical cells, with same current whether joined in series or parallel to a 1Ω resistor is​a)1 ohmb)0.5 ohmc)1.5 ohmd)2 ohmCorrect answer is 'A'. Can you explain this answer?
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