Question

Complete the following sentence: When multiple sources are connected together, their total e.m.f. will be equal to the sum of their individual e.m.fs if they are placed in ______ <, + explanation

Answer 1

Answer:- When they are placed in series.

When multiple emf sources are connected in series then the net or total emf is equal to the sum of their individual emfs .

Say if we have cells of emfs
`\epsilon_1` ,
`\epsilon_2` ,
`\epsilon_3` ,
`\epsilon_4` . . . .
`\epsilon_n`

Then the net emf is ,

`\implies \underline{\underline{\green{\epsilon_(net)= \epsilon_1+ \epsilon_2+\dots +\epsilon_n}}}\\`

Additional information:-

If the emfs of n cells are equal and they are connected in series then the net emf is given by ,

`\implies \epsilon_(net)= n\epsilon \\`

where ,

• 
  `\epsilon` = emf of a single cell .

Also , when n cells of emfs
`\epsilon_1` and
`\epsilon_2` . . . . .
`\epsilon_n` and internal resistances
`r_1` ,
`r_2` . . . . .
`r_n` respectively are connected in parallel then the net emf is given by,

`\implies \underline{\underline{\green{\epsilon_(net) = \left( (1)/(r_1)+(1)/(r_2)+\dots +(1)/(r_n)\right)^(-1)\left((\epsilon_1)/(r_1)+( \epsilon_2)/(r_2)+\dots +(\epsilon_n)/(r_n)\right)}}}\\`

Again suppose if we make a parallel arrangement of cells each having same emf then the net emf remains same that is equal to the emf of individual cell ( Why ? You can try yourself by using the above formula )

and we are done!