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Find equivalent emf of four different ce...

Find equivalent emf of four different cells which are connected in parallel. Their emf's and internal resistance are 1 volt, `1 Omega , 2` volt, `1 Omega,3` volt, `1Omega,4` volt, `2 Omega` and their connection is given below .

Text Solution

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From E `= ((E_(1))/(r_(1))+(E_(2))/(r_(2)))/((1)/(r_(1))+(1)/(r_(2)))" "r_(1) ^(')= (1)/((1)/(r_(1))+(1)/(r_(2))),r_(1)^(')=(1)/(2)`
For upper set, `E_(1)^(')= ((1)/(1)+(2)/(1))/((1)/(2)+(1)/(1))=(3)/(2)V`

For lower set `E_(2)^(')= ((4)/(2)-(3)/(2))/((1)/(2)+(1)/(1))= (-1)/((3)/(2))=(2)/(3)V,r_(2)^(')=(2)/(3)`
`E_(eq)=((E_(1)^('))/r_(1)^(')+(E_(2)^('))/(r_(2)^(')))/((1)/(r_(1)^('))+(1)/(r_(2)^(')))=(((3)/(2))/((1)/(2))-((2)/(3))/((2)/(3)))/((2)/(1)+(3)/(2))` ,brgt `E_(eq)= (4)/(7)V`
`r_(eq)= (1)/((1)/((1)/(2))+(1)/((2)/(3))) `
`= (1)/(2+(3)/(2))=(2)/(7) Omega `
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