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Five cells each of emf E and internal re...

Five cells each of emf E and internal resistance r send the same amount of current through an external resistance R whether the cells are connected in parallel or in series. Then the ratio `((R)/(r))` is

A

2

B

`1/2`

C

`1/5`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
Given: Number of cells, `n = 5`, emf of each cell `= E`
Internal resistance of each cell `= r`
In series, current through resistance R
`I= (nE)/( nr + R) = (5 E)/( 5 r + R)`
In parallel, current through resistance R
`I.= (E )/( (r)/( n) + R) = (n E)/ ( r + n R) = ( 5 E)/( r + 5 R)`
According to question, `I= I.`
`therefore (5 E)/ ( 5 r + 5 R) = ( 5 E)/( r + 5 R) rArr 5 r+ R = r + 5 R`
or `R = r therefore (R)/( r) = 1`
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