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Find the emf and internal resistance of ...

Find the emf and internal resistance of a single battery which is equivalent to a combination of three batteries as show in figure.

A

`20V, 2 Omega`

B

`0V, 2 Omega`

C

`3 V, 2 Omega`

D

`9 V, 2 Omega`

Text Solution

Verified by Experts

The correct Answer is:
C
The given combination consists of two batteries in parallel and resultant of these two batteries is in series with the third one.
For parallel combination we can apply,
`E_(eq)=((E_(1))/(r)-(E_(2))/r_(2))/((1)/(r_(1))+(1)/(r_(2)))=((10)/(2)-(4)/(2))/((1)/(2)+(1)/(2))=3V`
Further, `(1)/(r_(eq))=(1)/(r_(1))+(1)/(r_(2))=(1)/(2)+(1)/(2)=1" ":.r_(eq)=1Omega`
Now this is in series with the third one, i.e.,

The equivalent emf of these two is (6 – 3) V or 3 V and the internal resistance will be (1 + 1) or `2Omega`
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