Two cells of 1.5 V and 2 V , having internal resistances of `1Omega` and `2Omega` respectively, are connected in parallel so as to read the current in the same direction through an external resistance of `5 Omega` . The current in the external resistance will be

Options

A. `5/17 A`
B. `17/5 A`
C. `5/12 A`
D. `12/5 A`

Answer

A

Explanation

Applying K.V.L. for the loop ABCFA,
we have, `-1.5+I_(1)-2 I_(2)+2=0`
`I_(1)-2I_(2)=-0.5 ` ...(i)
By appling K.V.L. for the loop FCDEF,
we have, `-2+2I_(2)+5(I_(1)+I_(2))=0`
`5I_(1)+7I_(2)=2` .....(ii)
To solve equation (i) and (ii), multiply equation (i) by (7) and equation (ii) by (2), we have,
`{:(7I_(1)-14I_(2)=-3.5,),(10I_(1)+14I_(2)=4,),(bar(" "17I_(1)=0.5" "),):}`
`:.I_(1)=(0.5)/(17)=(1)/(34)A`
By substituting value of `I_(1)` in equation (ii), we have,
`I_(2)=(9)/(34)A`
`:.` Current through external resistance is,
`I_(1)+I_(2)=(1)/(34)+(9)/(34)=(10)/(34)=(5)/(17)A`